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question:f Ms. Jones received thank you cards from 30% of her class and 1/3 of these cards contained a 10 gift card, and she received a total of 50 in gift cards, how many students are there in her class?
answer:If Ms. Jones received thank you cards from 30% of her class, then the number of students who gave her cards is 30/100 * total number of students in her class. Let's call the total number of students x, so the number of students who gave her cards is 30/100 * x. If 1/3 of these cards contained a 10 gift card, then the number of cards with gift cards is 1/3 * (30/100 * x). The total value of the gift cards is 50, so 1/3 * (30/100 * x) * 10 = 50. Simplifying the equation, (1/3) * (3/10) * x * 10 = 50. Multiplying the fractions and simplifying further, 1/10 * x * 10 = 50. Multiplying both sides of the equation by 10, x = 50 * 10 / 10. Simplifying further, x = 50. Therefore, there are 50 students in Ms. Jones' class. 50 The answer is: 50
question:The base six number 53_{6} is equal to the base b number 113_{b}. What is the positive value of b?
answer:In base six, the number 53_{6} represents 5cdot6^1 + 3cdot6^0 = 33. In base b, the number 113_{b} represents 1cdot b^2 + 1cdot b^1 + 3cdot b^0 = b^2 + b + 3. Since 33 = b^2 + b + 3, we can rewrite this equation as b^2 + b - 30 = 0. Factoring, we get (b-5)(b+6) = 0. Since we are looking for a positive value of b, the only solution is b = boxed{5}. The answer is: 5
question:Koby and Cherie want to light fireworks. Koby has bought 2 boxes of fireworks while Cherie has just 1 box of fireworks. Koby’s boxes each contain 3 sparklers and x whistlers. Cherie’s box has 8 sparklers and 9 whistlers. In total, Koby and Cherie have 33 fireworks. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the number of whistlers in each of Koby's boxes. Let's break down the information given: Number of boxes of fireworks Koby has: 2 Number of sparklers in each of Koby's boxes: 3 Number of whistlers in each of Koby's boxes: x Number of sparklers in Cherie's box: 8 Number of whistlers in Cherie's box: 9 Total number of fireworks: 33 We can set up the equation as follows: (Number of boxes of fireworks Koby has * Number of sparklers in each of Koby's boxes) + (Number of boxes of fireworks Koby has * Number of whistlers in each of Koby's boxes) + Number of sparklers in Cherie's box + Number of whistlers in Cherie's box = Total number of fireworks (2 * 3) + (2 * x) + 8 + 9 = 33 Let's simplify and solve for x: 6 + 2x + 8 + 9 = 33 To isolate x, we subtract 23 from both sides of the equation: 2x + 23 - 23 = 33 - 23 2x = 10 Finally, we divide both sides of the equation by 2 to solve for x: x = 10 / 2 x = 5 The value of x is 5. 5 The answer is: 5
question:You walk twice as fast as Mr. Harris, and Mr. Harris took 2 hours to walk to the store. If your destination is x times further away than the store Mr. Harris walked to, how many hours will it take you to get there? If we know the answer to the above question is 3, what is the value of unknown variable x?
answer:We are given that Mr. Harris took 2 hours to walk to the store. We also know that you walk twice as fast as Mr. Harris, so it would take you half the time to walk the same distance. Therefore, it would take you 2/2 = 1 hour to walk to the store. If your destination is x times further away than the store Mr. Harris walked to, then it would take you x times longer to get there. So, the total time it would take you to get to your destination is 1 * x = x hours. We are given that the total time is 3 hours, so we can write: x = 3. The value of x is 3. 3 The answer is: 3