AMC10 2004 A

AMC10 2004 A · Q14

AMC10 2004 A · Q14. It mainly tests Averages (mean), Money / coins.

The average value of all the pennies, nickels, dimes, and quarters in Paula’s purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse?

Paula钱包里所有一分币、五分币、十分币和二十五分币的平均价值是20美分。如果她再多一枚二十五分币，平均价值将变为21美分。她钱包里有多少十分币？

(A) 0 0

(B) 1 1

(D) 3 3

(E) 4 4

Answer

Correct choice: (A)

正确答案：（A）

Solution

If $n$ is the number of coins in Paula’s purse, then their total value is $20n$ cents. If she had one more quarter, she would have $n+1$ coins whose total value in cents could be expressed both as $20n + 25$ and as $21(n + 1)$. Therefore $20n + 25 = 21(n + 1)$, so $n = 4$. Since Paula has four coins with a total value of 80 cents, she must have three quarters and one nickel, so the number of dimes is 0.

如果$n$是Paula钱包里的硬币数量，那么它们的总价值是$20n$美分。如果她再多一枚二十五分币，她将有$n+1$枚硬币，总价值（美分）既可表示为$20n+25$，也可表示为$21(n+1)$。因此$20n+25=21(n+1)$，所以$n=4$。由于Paula有四枚硬币，总价值80美分，她一定有三枚二十五分币和一枚五分币，因此十分币的数量是0。

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