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The product of three consecutive positive integers is times their sum. What is the sum of their squares? ' |
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Cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9 and then divided the result by 3, giving an answer of 43. What would her answer have been had she worked the problem correctly?
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Cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9 and then divided the result by 3, giving an answer of 43. What would her answer have been had she worked the problem correctly? |
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A football game was played between two teams, the Cougars and the Panthers. The two teams scored a total of 34 points, and the Cougars won by a margin of 14 points. How many points did the Panthers score? ' |
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Twenty percent off 60 is one-third more than what number? ' |
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Heather compares the price of a new computer at two different stores. Store offers off the sticker price followed by a rebate, and store offers off the same sticker price with no rebate. Heather saves by buying the computer at store instead of store . What is the sticker price of the computer, in dollars? ' |
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Let be the fixed fee, and be the amount she pays for the minutes she used in the first month. We want the fixed fee, which is |
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Let the three consecutive positive integers be , , and . So, . Rearranging and factoring, , so . Hence, the sum of the squares is . |
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We work backwards; the number that Cindy started with is . Now, the correct result is . Our answer is . |
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We work backwards; the number that Cindy started with is . Now, the correct result is . Our answer is . |
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Let be the number of points scored by the Cougars, and be the number of points scored by the Panthers. The problem is asking for the value of . |
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Twenty percent less than 60 is . One-third more than a number n is . Therefore and the number is . The answer is . |
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Solution 1The price of the computer is at store , and at store . Solving, we find , and the thus answer is . Solution 2The in store is better than the additional off at store . Thus the off is equal to , and therefore the sticker price is . |
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Understanding |
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