Question

Nevaeh has $4.75 worth of dimes and quarters. She has a total of 28 dimes and quarters altogether. Write a system of equations that could be used to determine the number of dimes and the number of quarters that Nevaeh has. Define the variables that you use to write the system.

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Answer 1

There are 15 dimes and 13 quarters.

Explanation:

Let d = number of dimes and q = number of quarters.

The number of dimes and quarters is 28:

d + q = 28

Solve for d:

d = 28 - q

Total dollar amount of dimes and quarters is $4.75 or 475 cents:

10d + 25q = 475

Substitute:

10(28 - q) + 25q = 475

280 - 10q + 25q = 475

15q = 475 - 280

15q = 195

q = 195/15

q = 13 quarters

Solve for d:

d = 28 - q

d = 28 - 13 = 15 dimes

Proof:

10d + 25q = 475

10(15) + 25(13) = 475

150 + 325 = 475

475 = 475

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