2004 AMC 10A Problem 14

Below is the professionally curated solution for Problem 14 of the 2004 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2004 AMC 10A solutions, or check the answer key.

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Concepts:mean money linear equation

Difficulty rating: 1450

14.

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?

$0$

$1$

$2$

$3$

$4$

Solution:

With $n$ coins the total value is $20n$ cents. Adding a quarter gives $20n + 25 = 21(n + 1),$ so $n = 4.$

Four coins worth a total of $80$ cents must be three quarters and one nickel. Hence the number of dimes is $0.$

Thus, the correct answer is A.

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