Question

You have 59 total coins in a jar on your nightstand at home. The total amount of money is $12.05. You only have quarters and dimes. How many of each type of coin do you have? (hint - use a different method to write and solve the system).​

Answer 1

9514 1404 393

Answer:

• 41 quarters
• 18 dimes

Explanation:

When there are two contributors to the mix, it usually works well to let a variable represent the quantity of the larger contributor. Here, that larger contributor is the quarter.

Let q represent the number of quarters. Then 59-q is the number of dimes. The value of the coins, in cents, is ...

25q +10(59 -q) = 1205

15q +590 = 1205 . . . . . . . . eliminate parentheses, collect terms

15q = 615 . . . . . . . . . . . subtract 590

q = 41 . . . . . . . . . . divide by 15

59-q = 59 -41 = 18 . . . . . number of dimes

You have 41 quarters and 18 dimes.