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SOURCE:COMPETITION Number of Problems: 9. FOR PRINT ::: (Book)
Chandra pays an on-line service provider a fixed monthly fee plus an hourly charge for connect time. Her December bill was , but in January her bill was because she used twice as much connect time as in December. What is the fixed monthly fee?
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
The product of three consecutive positive integers is times their sum. What is the sum of their squares?
Let the three consecutive positive integers be , , and . So, . Rearranging and factoring, , so . Hence, the sum of the squares is .
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?
We work backwards; the number that Cindy started with is . Now, the correct result is . Our answer is .
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?
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 .
Twenty percent off 60 is one-third more than what number?
Twenty percent less than 60 is . One-third more than a number n is . Therefore and the number is . The answer is .
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?
Let the sticker price be .
The price of the computer is at store , and at store .
Heather saves at store , so .
Solving, we find , and the thus answer is .
The in store is better than the additional off at store .
Thus the off is equal to , and therefore the sticker price is .