2004 AMC 12A Problem 11

Question

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

Let

n

be the current number of coins and write the total value two ways after adding a quarter

Solve

20n + 25 = 21(n + 1)

for

n,

then figure out which coins total

20n

cents

If Paula has

n

coins, their total value is

20n

cents. Adding a quarter gives

n + 1

coins worth

20n + 25

cents, which must also equal

21(n + 1)

cents.

So

20n + 25 = 21(n + 1),

giving

n = 4.

Four coins totalling

80

cents must be three quarters and one nickel, so the number of dimes is

0.

Thus, the correct answer is A.

Problem 11 in other years