Number of quarters and dimes equals

Question

A man has 22 coins in his pocket, all of which are dimes and quarters. If the total value of his

change is 370 cents, how many dimes and how many quarters does he have?

Your answer is

number of dimes equals

number of quarters equals

Answer 1

This is a common question type for Algebra 1 that can be solved by setting up a system of linear equations. The question guides you to see that we have two unknowns: the # of each type of coin. We will be able to set up one equation using the total number of coins, and set up a second equation by using the total value:

Let d: # of dimes ; q: # of quarters

d + q = 22

10d + 25q = 370 Multiply 1st equation by - 10. Then add the 2 eqns, left side to left side, right to right:

-10d - 10q = - 220 (This technique is known as elimination. Substitution would also work well here.)

__________________

15q = 150

q = 10 ; d = 12