2004 AMC 12A Problems/Problem 11

Problem

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?

$\text {(A)}\ 0 \qquad \text {(B)}\ 1 \qquad \text {(C)}\ 2 \qquad \text {(D)}\ 3\qquad \text {(E)}\ 4$

Solution

Let the total value (in cents) of the coins Paula has originally be $x$ , and the number of coins she has be $n$ . Then $\frac xn = 20 \Longrightarrow x = 20n$ and $\frac {x+25}{n+1} = 21$ . Substituting yields $20n + 25 = 21(n+1) \Longrightarrow n = 4, x = 80$ . It is easy to see now that Paula has 3 quarters, 1 nickel, so she has $0\ \mathrm{(A)}$ dimes.

2004 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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2004 AMC 12A Problems/Problem 11

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