Question

In a child's bank are 11 coins that have a value of S1.85. The coins are either

quarters or dimes. How many coins each does child have?
a. Define your variables:
b. Write the equations:
d. Check:
c. Solve:

Answer 1

The child has 6 dimes and 5 quarters.

Explanation:

Let q and d represent the number of quarters and of dimes respectively.

Then q + d = 11 (Equation A), and ($0.25/quarter)q + ($0.10/dime)d = $1.85 (Equation B).

Multiply the 2nd equation by 100 to remove the decimal fractions:

25q + 10d = 185 (Equation C)

Now multiply the 1st equation by -10 to obtain -10q - 10d = -110 (Equation D), and combine this result with Equation C:

-10q - 10d = -110

25q + 10d = 185

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15q = 75, and so q = 75/15 = 5.

According to Equation A, q + d = 11. Replacing q with 5, we get:

5 + d = 11, and so d = 6.

The child has 6 dimes and 5 quarters.