conversations listlengths 2 2 | source stringclasses 1 value | stack stringclasses 1 value |
|---|---|---|
[
{
"from": "human",
"value": "If Janice gave away all three dozens of pebbles from her trip and each of her friends received 4 pebbles, how many friends received pebbles?"
},
{
"from": "gpt",
"value": "Three dozens of pebbles mean 3 x 12 = 36 pebbles.\nIf each friend received 4 pebbles, then the ... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If the best-selling book, \"TOP,\" costs $8 and the least-selling book, \"ABC,\" costs $23, and last week 13 \"TOP\" books and 4 \"ABC\" books were sold, what is the difference in earnings for these two books at the bookstore last week?"
},
{
"from": "gpt",
"value": ... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "In a class of $40$ students, X said they liked apple pie, $15$ said they liked chocolate cake, and $12$ said they did not like either. There are 5 students in the class who liked both. What is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "To solve t... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If it takes 1 hour for Rob to get to the national park and three times as much time for Mark to get there, and Rob leaves his home at 11 a.m., what time should Mark leave his home so that they both arrive at the national park at the same time?"
},
{
"from": "gpt",
"v... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "A box of ice cream bars costs $7.50 and contains three bars. 6 friends want to each eat 2 bars. How much money will that require per person?"
},
{
"from": "gpt",
"value": "A box of ice cream bars costs $7.50 and contains 3 bars, so each bar costs $7.50/3 = $2.50\n6... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "What is the smallest positive integer $x$ that, when multiplied by $400$, produces a product that is a multiple of $576$?"
},
{
"from": "gpt",
"value": "We want to find the smallest positive integer $x$ such that $400x$ is a multiple of $576$.\nSince $576$ is divisib... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "What is the value of $9^3 + 3(9^2) + 3(9) + X$? The answer is 1000. What is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "To solve this problem, we need to determine the value of x, which represents the unknown variable in the expression.\nThe given... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If Mike spent a total of 37 dollars on 12 notebooks, and he bought 3 red notebooks at 4 dollars each, 2 green notebooks at 2 dollars each, and the rest were blue notebooks, what is the cost of each blue notebook?"
},
{
"from": "gpt",
"value": "Mike spent a total of 3... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Tara has been planning to buy a laptop which costs $1000. A computer shop accepts payment in installments of $65 per month provided that a 20% down payment is made. If Tara wants to pay an additional $20 for the down payment, how much will her balance be after paying for 4 month... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Claire won a $100 gift card to her favorite coffee shop. She wants to treat herself to a latte that cost $3.75 and a croissant for $3.50 every morning for a week. She also plans to buy 5 cookies that cost $1.25 each. How much money will be left on her card after a week of coffe... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If a large puzzle costs $15 and a small puzzle and a large puzzle together cost $23, what would be the total cost of 1 large puzzle and 3 small puzzles?"
},
{
"from": "gpt",
"value": "Let's assume the cost of the small puzzle is S.\nAccording to the given information... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Neil charges $5.00 to trim up each boxwood. He charges $15.00 to trim it into a fancy shape. The customer wants the entire 30 boxwood hedge trimmed up. He has also asked for 4 specific boxwoods shaped into spheres. How much will Neil charge?"
},
{
"from": "gpt",
... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "In the second week of June, Xenia worked 22 hours and earned $47.60 more than she did in the first week when she worked 15 hours. Assuming her hourly wage remained constant, what was her total earnings for the first two weeks of June, rounded to the nearest hundredth?"
},
{
... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Define $a * b$ as $2a - b^2$. If $a * 5 = 9$, what is the value of $a$?"
},
{
"from": "gpt",
"value": "We are given that $a * 5 = 2a - 5^2 = 9$.\nSimplifying, we have $2a - 25 = 9$.\nAdding 25 to both sides, we get $2a = 34$.\nDividing both sides by 2, we find $a = \... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Olivia bought two packs of basketball cards at $3 each, and 5 decks of baseball cards at $4 each. If she had one $50 bill, how much change did she receive?"
},
{
"from": "gpt",
"value": "Two packs of basketball cards at $3 each cost 2 * $3 = $6\nFive decks of baseba... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Jane is shopping for some fruit. She sees a stand of fruit advertising x apples for $2, and another one advertising 5 oranges for $1.50. Assuming there's no price discount for buying in bulk, Jane would spend 240 cents if she bought 12 of the cheaper of the two fruits. What is... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Steve wanted to make a total of $100 within four days, so he took on a berry-picking job in Sweden. The job paid $2 for every pound of lingonberries picked. On Monday he picked 8 pounds. Tuesday’s harvest was triple what he had picked the previous day. On Wednesday he felt very ... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "A bag full of sugar weighs 16 kg. A bag full of salt weighs 30 kg. If you remove 4 kg from the combined weight of these two bags, how much do the bags now weigh?"
},
{
"from": "gpt",
"value": "The combined weight of the two bags is 16 kg + 30 kg = 46 kg\nIf you remov... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "In a newspaper, each one of 12 pages holds 2 photos and each of another 9 pages hold 3 photos. How many photos are used in the newspaper?"
},
{
"from": "gpt",
"value": "There are 12 pages with 2 photos each, so 12 x 2 = 24 photos on those pages.\nThere are 9 pages wi... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Karen works at an animal shelter with 30 dogs, 28 cats, and 20 lizards. Every month, 50% of the dogs are adopted, 25% of the cats are adopted, and 20% of lizards are adopted. If the shelter takes in 13 new pets a month, how many pets are there after x month?\nIf we know the answ... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Darma can eat 20 peanuts in 15 seconds. At this same rate, She could eat 480 peanuts in x minutes. What is the value of unknown variable x? What is the value of unknown variable x?"
},
{
"from": "gpt",
"value": "To solve this problem, we need to determine the value o... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Eva learns for two semesters in a year. In 2019, she scored ten more marks in maths in the first semester than the second, 15 marks less in arts, and 1/3 marks less in science in the first semester than the second. If she got 80 marks in maths in the second semester, 90 marks in... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Sam is serving spaghetti and meatballs for dinner. The pasta costs $1.00 per box, a jar of sauce is $2.00 and 1 pound of meatballs is $5.00. He wants to stretch this meal into 8 servings. How much does each serving cost?"
},
{
"from": "gpt",
"value": "The cost of ... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If James initially buys 100 tennis balls and gives away half of them, how many tennis balls does he put into each of the 5 large containers?"
},
{
"from": "gpt",
"value": "James initially has 100 tennis balls\nHe gives away half of them, so he has 100/2 = 50 tennis b... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Barney the dinosaur weighs 1500 pounds more than five regular dinosaurs combined. If each regular dinosaur weighs x pounds, find the combined weight of Barney and the five regular dinosaurs' weights?\nIf we know the answer to the above question is 9500, what is the value of unkn... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "When a polynomial is divided by $-3x^5 + 10x - 11,$ what are the possible degrees of the remainder? Enter all the possible values, separated by commas."
},
{
"from": "gpt",
"value": "When a polynomial is divided by $-3x^5 + 10x - 11,$ the remainder will have a degre... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If $g(x) = 3x + 7$ and $f(x) = 5x - X$, what is the value of $f(g(8))$?\nIf we know the answer to the above question is 146, what is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "We are given the functions $g(x) = 3x + 7$ and $f(x) = 5x - X$.\nTo fi... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Find the minimum value of\n\\[\\frac{x^2}{x - 8}\\]for $x > X The answer is 32. What is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "To find the minimum value of the expression, we need to find the value of x that makes the denominator, x - 8, as s... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Let $C$ be the circle with equation $x^2+12y+57=-y^2-10x$. If $(a,b)$ is the center of $C$ and $r$ is its radius, what is the value of $a+b+r$?"
},
{
"from": "gpt",
"value": "We rewrite the equation as $x^2+10x+y^2+12y=-57$.\nCompleting the square for $x$ and $y$, we... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Find the product of all constants $t$ such that the quadratic $x^2 + tx - 10$ can be factored in the form $(x+a)(x+b)$, where $a$ and $b$ are integers."
},
{
"from": "gpt",
"value": "If the quadratic can be factored as $(x+a)(x+b)$, then the constant term is $ab=-10$... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Calculate the value of $\\left(\\frac{7}{8}\\right)^3 \\cdot \\left(\\frac{7}{8}\\right)^{-3}$."
},
{
"from": "gpt",
"value": "Recall that when we multiply two numbers with the same base, we add their exponents.\nSo, $\\left(\\frac{7}{8}\\right)^3 \\cdot \\left(\\fra... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "James paints a 20 ft by 15 ft mural. It takes him 20 minutes to paint 1 square foot and he charges $x per hour. How much does he charge to paint the mural?\nIf we know the answer to the above question is 15000, what is the value of unknown variable x?"
},
{
"from": "gp... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Thomas owns 200 books. He decides to sell them and use the money to buy records. Each book sells for $1.5. A record costs $3. If he buys 75 records, how much money does he have left over?"
},
{
"from": "gpt",
"value": "Thomas has 200 books and each book sells for $1.... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If Betty picked 16 strawberries, Matthew picked 20 more than Betty and twice as many as Natalie. They used these strawberries to make jam, with each jar requiring 7 strawberries. They sold each jar for $4. What is the total amount of money they made from the strawberries they pi... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Mona plays a multiplayer video game on the weekends. She joins groups with four other players to complete objectives in the game. The past weekend, she joined 9 groups. One of the groups included two players she had grouped with before that weekend, and another group included on... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If there are 5 big boxes, each containing 7 dolls, and 9 small boxes, each containing 4 dolls, what is the total number of dolls?"
},
{
"from": "gpt",
"value": "If there are 5 big boxes, each containing 7 dolls, then there are 5 x 7 = 35 dolls in the big boxes.\nIf t... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "In the diagram, $PQRS$ is a trapezoid with an area of $12.$ $RS$ is twice the length of $PQ.$ What is the area of $\\triangle PQS?$\n\n[asy]\ndraw((0,0)--(1,4)--(7,4)--(12,0)--cycle);\ndraw((7,4)--(0,0));\nlabel(\"$S$\",(0,0),W);\nlabel(\"$P$\",(1,4),NW);\nlabel(\"$Q$\",(7,4),NE... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "What is the 100th digit after the decimal point of the decimal representation of 1/7?"
},
{
"from": "gpt",
"value": "We know that $\\frac{1}{7}$ is a repeating decimal with a repeating block of 6 digits: 142857.\nTo find the 100th digit after the decimal point, we ca... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Given a square with an area of 81 square units, each side is divided into 3 equal parts by drawing two points on each side. The figure is then formed by connecting the points on adjacent sides with quarter-circle arcs. What is the length of the perimeter of the bolded figure, ro... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "A store ordered 300 more than twice as many pens as it did pencils at $5 each. If the cost of a pencil was $4, and the store ordered x boxes, each having 80 pencils, calculate the total amount of money they paid for the stationery.\nIf we know the answer to the above question is... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If the sum of two numbers is 30, and we double the larger number and subtract three times the smaller number, the result is 5. What is the positive difference between the two numbers?"
},
{
"from": "gpt",
"value": "Let the two numbers be $x$ and $y$, with $x>y$.\nFro... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If there are 6 triangle-shaped cookie cutters, 4 square ones, and 2 hexagons in the drawer, what is the total number of sides on all the cookie cutters?"
},
{
"from": "gpt",
"value": "Each triangle has 3 sides, so 6 triangles have 6 * 3 = 18 sides.\nEach square has 4... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If Jaxon received 15 toys and Gabriel has twice as many toys as Jaxon, while Jerry has 8 more toys than Gabriel, what is the total number of toys that Jerry, Gabriel, and Jaxon have together?"
},
{
"from": "gpt",
"value": "Jaxon received 15 toys.\nGabriel has twice a... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If Patricia has 4 empty barrels, each with a capacity of 7 gallons, and there is a faucet with a flow rate of 3.5 gallons per minute, how many minutes will it take to fill all 4 barrels?"
},
{
"from": "gpt",
"value": "Each barrel has a capacity of 7 gallons, so 4 bar... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "What is $(5^{-2})^0 + (5^0)^3$?"
},
{
"from": "gpt",
"value": "$5^{-2} = \\frac{1}{5^2} = \\frac{1}{25}$,\nso $(5^{-2})^0 = \\left(\\frac{1}{25}\\right)^0 = 1$.\n\n$5^0 = 1$,\nso $(5^0)^3 = 1^3 = 1$.\n\nTherefore, $(5^{-2})^0 + (5^0)^3 = 1 + 1 = \\boxed{2}$.\nThe ans... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Let $P$ be a point on the line\n\\[\\begin{pmatrix} 3 \\\\ -1 \\\\ X \\end{pmatrix} + t \\begin{pmatrix} 2 \\\\ -2 \\\\ 1 \\end{pmatrix}\\]and let $Q$ be a point on the line\n\\[\\begin{pmatrix} 0 \\\\ 0 \\\\ 4 \\end{pmatrix} + s \\begin{pmatrix} 1 \\\\ 2 \\\\ -1 \\end{pmatrix}.... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Determine the largest prime factor of 1337."
},
{
"from": "gpt",
"value": "We can start by factoring out the smallest prime factor, which is 7.\n$1337 = 7 \\times 191$\nSince 191 is a prime number, the largest prime factor of 1337 is $\\boxed{191}$.The answer is: 191... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "What is the number of one-fourths in $\\frac{7}{2}$?"
},
{
"from": "gpt",
"value": "To find the number of one-fourths in $\\frac{7}{2}$, we can divide $\\frac{7}{2}$ by $\\frac{1}{4}$.\nDividing $\\frac{7}{2}$ by $\\frac{1}{4}$ is the same as multiplying $\\frac{7}{2... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Victoria had $500. She went to the market and bought 2 packets of rice each at $20, 3 packets of wheat flour each at x, and 1 soda at $150. What was her remaining balance?\nIf we know the answer to the above question is 235, what is the value of unknown variable x?"
},
{
... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If James purchased a gallon of milk for $3, a bunch of bananas for $2, and paid 20% sales tax, what is the total amount of money that he spent?"
},
{
"from": "gpt",
"value": "The cost of the milk is $3.\nThe cost of the bananas is $2.\nTo calculate the sales tax, we ... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "For what value of $x$ does $3^{2x^{2}-5x+2} = 3^{2x^{2}+7x-4}$? Express your answer as a common fraction."
},
{
"from": "gpt",
"value": "Since the bases are equal, we can set the exponents equal to each other.\nSo we have $2x^{2}-5x+2 = 2x^{2}+7x-4$.\nSimplifying, we... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Cody was reading through his favorite book series. The series was 54 books in total. If Cody read 6 books the first week, and x books the second week and then 9 books every week after that. How many weeks did it take Cody to read his series?\nIf we know the answer to the abov... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "After working for Mrs. Jane, Jason was paid 60 more coins than Jayden. If Jayden received x coins, how many coins did Mrs. Jane gave 660 to the boys in total. What is the value of unknown variable x?"
},
{
"from": "gpt",
"value": "To solve this problem, we need to de... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Sandy bought 1 million Safe Moon tokens. She has x siblings. She wants to keep half of them to herself and divide the remaining tokens among her siblings. After splitting it up, how many more tokens will she have than any of her siblings?\nIf we know the answer to the above ques... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "A designer has X fabric colors he may use for a dress: red, green, and blue. Four different patterns are available for the dress. If each dress design requires exactly one color and one pattern, There are 12 different dress designs possible. What is the value of unknown variable... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "On a shopping trip in a crowded store, Josie had to wait 3 minutes for a cart, 13 minutes for an employee to unlock a cabinet to get her a product, 14 minutes for a stocker to restock a shelf with what she wanted, and x minutes in line to check out. Her shopping trip took an hou... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Determine the value of the expression $(25 + 8)^2 - (8^2 + 25^2)$."
},
{
"from": "gpt",
"value": "We can simplify the expression by using the formula for the difference of squares.\n$(25 + 8)^2 - (8^2 + 25^2) = (33)^2 - (64 + 625) = 1089 - 689 = \\boxed{400}$.\nThe a... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Dana Point beach has four times the number of sharks as Newport Beach. If Newport Beach has 22 sharks, how many sharks are there in total on the two beaches?"
},
{
"from": "gpt",
"value": "If Newport Beach has 22 sharks, then Dana Point beach has 4*22 = 88 sharks.\nT... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "There are 50 children at the party. Three-fifths of them are boys. How many of the children are girls?"
},
{
"from": "gpt",
"value": "If three-fifths of the children are boys, then two-fifths must be girls.\nTwo-fifths of 50 children is (2/5) * 50 = 20\nTherefore, th... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If Sally purchased three photograph frames, each for $3, and paid with a $20 bill, how much change did she receive?"
},
{
"from": "gpt",
"value": "Sally purchased 3 photograph frames for $3 each, so the total cost is 3 * $3 = $9\nShe paid with a $20 bill, so her chan... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "A rectangular room measures 12-feet by 6-feet. How many square yards of carpet are needed to cover the floor of the room?"
},
{
"from": "gpt",
"value": "First, we need to convert the measurements to the same unit. Since we need to find the area in square yards, we ne... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Carolyn practices the piano for 20 minutes a day and the violin for three times as long. If she practice six days a week, how many minutes does she spend practicing in a month with four weeks?"
},
{
"from": "gpt",
"value": "Carolyn practices the piano for 20 minutes ... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "What is the base 10 value of the number $135_7$?"
},
{
"from": "gpt",
"value": "To convert a number from base $b$ to base 10, we multiply each digit by $b$ raised to the corresponding power and sum them up.\nIn this case, we have $1 \\cdot 7^2 + 3 \\cdot 7^1 + 5 \\cd... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Calculate $\\sqrt{30p} \\cdot \\sqrt{5p} \\cdot \\sqrt{6p}$ . Express your answer in simplest radical form in terms of $p$."
},
{
"from": "gpt",
"value": "Using the property $\\sqrt{ab} = \\sqrt{a} \\cdot \\sqrt{b}$ and the fact that $\\sqrt{a^2} = a$, we have: \n\n$... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Tom went to the store to buy fruit. Lemons cost x, papayas cost $1, and mangos cost $4. For every 4 fruits that customers buy, the store offers a $1 discount. Tom buys 6 lemons, 4 papayas, and 2 mangos. He will pay 21. What is the value of unknown variable x?"
},
{
"from... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If each man at a party danced with exactly three women and each woman danced with exactly two men, and there were twelve men at the party, how many women attended the party?"
},
{
"from": "gpt",
"value": "Each man danced with exactly three women, so there were $12 \\... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Madison makes 30 paper boats and sets them afloat. 20% are eaten by fish and Madison shoots x of the others with flaming arrows. There are 22 boats left. What is the value of unknown variable x?"
},
{
"from": "gpt",
"value": "To solve this problem, we need to determi... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Simplify the expression $\\frac{\\sqrt{507}}{\\sqrt{48}} - \\frac{\\sqrt{175}}{\\sqrt{112}}$."
},
{
"from": "gpt",
"value": "We can simplify the expression by rationalizing the denominators.\nFirst, we simplify the radicals in the denominators:\n$\\sqrt{48} = \\sqrt{... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "What is the remainder when $1 + 2 + 3 + 4 + \\dots + 9 + 10$ is divided by 8?"
},
{
"from": "gpt",
"value": "We can rewrite the sum as $(1+2+3+4+5) + (6+7+8+9+10)$.\nThe sum of the first 5 positive integers is $1+2+3+4+5 = 15$.\nThe sum of the next 5 positive intege... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If $x$ is doubled, increased by $3$, and then divided by $5$, the result is $11$. What is the value of $x$?"
},
{
"from": "gpt",
"value": "Let $y$ be the value after doubling $x$, increasing by $3$, and then dividing by $5$.\nWe can write this as $y = \\frac{2x + 3}{... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "What is the value of y that makes the vectors $\\begin{pmatrix} 1 \\\\ -3 \\\\ -4 \\end{pmatrix}$ and $\\begin{pmatrix} -2 \\\\ y \\\\ -1 \\end{pmatrix}$ orthogonal?"
},
{
"from": "gpt",
"value": "Two vectors are orthogonal if their dot product is equal to 0.\nSo, we... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "What is the total amount spent by all the ladies on dresses, considering that Patty's dress cost $10 more than Ida's, Ida's dress cost $30 more than Jean's, Jean's dress cost $10 less than Pauline's, and Pauline's dress cost $30?"
},
{
"from": "gpt",
"value": "Paulin... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Joan is at the grocery store. She has a total of $60 to spend. She is going to purchase 2 containers of hummus, which are $5 each. She is going to purchase chicken for $20, bacon for $10, and vegetables for $10. She wants to purchase apples which are $2 each. With her remaining ... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If Samuel finished his homework in 30 minutes and Sarah took 1.3 hours to finish it, how many minutes faster did Samuel finish his homework compared to Sarah?"
},
{
"from": "gpt",
"value": "Samuel finished his homework in 30 minutes.\nSarah took 1.3 hours to finish h... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If vectors a and b are nonzero and satisfy ||a + b|| = ||a - b||, what is the angle between vectors a and b in degrees?"
},
{
"from": "gpt",
"value": "We start with the given equation $||a + b|| = ||a - b||$.\nBy squaring both sides, we get $(a + b) \\cdot (a + b) = ... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "How many prime numbers are between 20 and 30?"
},
{
"from": "gpt",
"value": "We can check each number between 20 and 30 to see if it is prime.\nChecking each number individually, we find that the prime numbers between 20 and 30 are 23, 29.\nSo, there are $\\boxed{2}$... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Goldie makes $5 an hour for pet-sitting. Last week, she worked for x hours while this week, she worked for 30 hours. How much did Goldie earn in two weeks for pet-sitting?\nIf we know the answer to the above question is 250, what is the value of unknown variable x?"
},
{
... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Olivia and Nigel are traveling in Asia. Olivia has $112 and Nigel has $139. If together they buy six one day passes to a tourist attraction for $28 per ticket, how much money do they have left?"
},
{
"from": "gpt",
"value": "Olivia has $112 and Nigel has $139, so th... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Over the course of the week, Doug has extinguished 20 fires, while Kai has extinguished three times as many fires as Doug. Additionally, Eli has extinguished half the number of fires that Kai has. What is the total number of fires that they have extinguished for the entire week?... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "A local business sold 25 raffle tickets at $2.00 each to raise money for charity. In addition, they received two $15 donations and one $20 donation. What is the total amount of money that they raised?"
},
{
"from": "gpt",
"value": "The business sold 25 raffle tickets... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "A desert garden’s sprinkler system runs twice a day during the cool morning and evening hours. It waters the garden with x liters of water in the morning and six liters in the evening. The sprinkler system takes 5 days to use 50 liters of water. What is the value of unknown vari... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "On Monday, Jasmine had 2 paperclips. The number of paperclips she had on Tuesday was 6, and each day after that, the number of paperclips tripled. On which day of the week did she first have more than 100 paperclips?"
},
{
"from": "gpt",
"value": "On Tuesday, Jasmine... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Find the integer $n$, $0 \\le n \\le 11$, such that \\[n \\equiv 10389 \\pmod{12}.\\]"
},
{
"from": "gpt",
"value": "We can find the remainder when 10389 is divided by 12 by dividing the hundreds digit by 12, which is 8, and multiplying by 12 to get 96. Subtracting t... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Hendricks buys a guitar for x, which is 20% less than what Gerald bought the same guitar for. Gerald paid 250 for his guitar. What is the value of unknown variable x?"
},
{
"from": "gpt",
"value": "To solve this problem, we need to determine the value of x, which rep... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Nathaniel has x tickets to a basketball game. He gives away 2 tickets each to his best friends, until he only has 3 tickets left. Nathaniel has 4 best friends. What is the value of unknown variable x?"
},
{
"from": "gpt",
"value": "To solve this problem, we need to d... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Madeline wants to drink 100 ounces of water in a day. Her water bottle can hold 12 ounces of water. She refills her water bottle 7 times. How much more water does she need to drink?"
},
{
"from": "gpt",
"value": "Madeline's water bottle can hold 12 ounces of water an... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "In how many ways can I choose a 4-person committee from a club of X people? The answer is 126. What is the value of unknown variable X?"
},
{
"from": "gpt",
"value": "To solve this problem, we need to determine the value of x, which represents the number of people in... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "A fruit and vegetable merchant installed 15 kg of carrots, 13 kg of zucchini and 8 kg of broccoli. He sold only x% of them. He sold 18 mass of vegetables. What is the value of unknown variable x?"
},
{
"from": "gpt",
"value": "To solve this problem, we need to determ... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Pete walks backwards three times faster than Susan walks forwards, and Tracy does one-handed cartwheels twice as fast as Susan walks forwards. But Pete can walk on his hands only one quarter the speed that Tracy can do cartwheels. If Pete walks on his hands at 2 miles per hour... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Find all values of $a$ so that the lines specified by\n\\[\\begin{pmatrix} 1 \\\\ 2 \\\\ a \\end{pmatrix} + t \\begin{pmatrix} X \\\\ 3 \\\\ 4 \\end{pmatrix}\\]and\n\\[\\begin{pmatrix} 4 \\\\ 1 \\\\ 0 \\end{pmatrix} + u \\begin{pmatrix} 5 \\\\ 2 \\\\ 1 \\end{pmatrix}\\]are skew.... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "For a finite sequence $A=(a_1,a_2,\\dots,a_n)$ of numbers, the Cesaro sum of $A$ is defined to be\n\\[\\frac{S_1+\\cdots+S_n}{n},\\]where $S_k=a_1+\\cdots+a_k$ and $1\\leq k\\leq n$.\n\nIf the Cesaro sum of the 99-term sequence $(a_1,\\dots,a_{99})$ is X, what is the Cesaro sum... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If $x - y = 6$ and $x + y = 12$, what is the value of $y$?"
},
{
"from": "gpt",
"value": "We can add the two equations to eliminate $y$, giving $2x = 18$, so $x = 9$.\nSubstituting this value back into either equation, we find $9 + y = 12$, so $y = \\boxed{3}$.\nThe ... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If a teacher teaches 5 periods a day and works for 24 days in a month, earning $5 per period, and has been working for 6 months, what is the total amount he has earned?"
},
{
"from": "gpt",
"value": "The teacher teaches 5 periods a day, so the teacher earns 5 periods... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If Doris puts 3 widgets in each carton, which is 4 inches wide, 4 inches long, and 5 inches tall, and then packs those cartons into a shipping box that is 20 inches wide, 20 inches long, and 20 inches high, how many widgets can be shipped in each shipping box?"
},
{
"fro... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Our water polo team has 15 members. I want to choose a starting team consisting of 7 players, one of whom will be the goalie (the other six positions are interchangeable, so the order in which they are chosen doesn't matter). In how many ways can I choose my starting team?"
... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "If Karen works at an animal shelter with 30 dogs, 28 cats, and 20 lizards, and every month, 50% of the dogs, 25% of the cats, and 20% of the lizards are adopted, with the addition of 13 new pets, what is the total number of pets in the shelter after one month?"
},
{
"fro... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Calculate the value of $f(g(4))-g(f(4))$ given that $f(x) = x + 3$ and $g(x) = 3x + 5$."
},
{
"from": "gpt",
"value": "First, we find $g(4)$ by substituting $x=4$ into the expression for $g(x)$:\n$$g(4) = 3(4) + 5 = 12 + 5 = 17.$$\nNext, we find $f(4)$ by substitutin... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Carrie is making punch. She adds 6 12-oz cans of Mountain Dew, 28 oz of ice, and a 40 oz bottle of fruit juice. How many 10 oz servings of punch does Carrie have?"
},
{
"from": "gpt",
"value": "Carrie adds 6 cans of Mountain Dew, which are each 12 oz, so 6 x 12 = 72 ... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "Sunnyvale School was having a picnic. They wanted to make fruit punch. They had x liters of orange punch. They had twice as much cherry punch as orange punch and 1.5 liters less of apple juice than cherry punch. When they combined all of the fruit juices together, how many liter... | MetaMathQA | chosen |
[
{
"from": "human",
"value": "James decides to start making his own coffee. He buys a coffee machine for $200 and gets a $20 discount. He figures it will cost him $3 a day to make his coffee. He previously bought 2 coffees a day for $4 each. How long until the machine pays for itself?"
},
{
"fro... | MetaMathQA | chosen |
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