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 money linear equation

Difficulty rating: 1450

Solution:

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

If there were at most two quarters, the other coins would be worth at most $10$ cents each, so four coins would total at most $2(25)+2(10)=70$ cents. Thus there must be three quarters, leaving $5$ cents for the fourth coin. The purse contains three quarters and one nickel, so it has $0$ dimes.

Thus, the correct answer is A.

2004 AMC 10A Problem 14

Answer: A

Difficulty rating: 1450

Solution:

Problem 14 in Other Years