## A collection of quarters and dimes has a total value of$5.00 and contains 32 coins. How many of each kind of coins are there in the collecti Question A collection of quarters and dimes has a total value of$5.00 and contains 32 coins. How many of each kind of coins are there in the collection?

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6 months 2021-07-17T10:22:10+00:00 1 Answers 5 views 0

1. 9514 1404 393

12 quarters

20 dimes

Step-by-step explanation:

If all were dimes the value would be $3.20. It is$1.80 more than that. Each replacement of a dime with a quarter adds $0.15 to the value, so there must be$1.80/\$0.15 = 12 such replacements.

There are 12 quarters and 20 dimes.

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Let q represent the number of quarters.

0.25q +0.10(32 -q) = 5.00 . . . . . total value

0.15q +3.20 = 5.00 . . . . . . . . . simplify

q = (5.00 -3.20)/0.15 . . . . . . subtract 3.20 and divide by 0.15

q = 12