# a bank contains 27 coins consisting of dimes and quarters. the coins have a total value of \$4.95. Find the number of dimes and quarters in the bank.

Answer: 12 dimes and 15 quarters
12 quarters and 10 dimes to make 4 dollars and
3 quarters and 2 dimes to make 95 cents

The bank has 15 quarters and 12 dimes.

### Explanation:

This problem can be solved using systems of equations. Let's define the variables: let D represent the number of dimes and Q represent the number of quarters.

From the problem, we have two equations:

• D + Q = 27 (the total number of coins)
• 0.10D + 0.25Q = 4.95 (the total value of the coins)

Multiply the first equation by 0.10 to make the coefficients of D the same in both equations:

• 0.10D + 0.10Q = 2.70

Subtract this from the second equation to find Q:

• 0.15Q = 2.25. Consequently, Q = 15 quarters.

Substitute Q = 15 into the first equation to find D:

• D + 15 = 27, hence D = 12 dimes.

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