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?

$0$

$1$

$2$

$3$

$4$

Answer: A

Concepts:mean linear equation

Difficulty rating: 1420

Solution:

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.

2004 AMC 12A Problem 11

Answer: A

Difficulty rating: 1420

Solution:

Problem 11 in Other Years