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This is a system of equations.

Let d= number of dimes.

q= number of quarters.

d+q=1000 -> 10d + 10q = 10000

.10d+.25q=199.90-> -10d+(-25q)=-19990

Multiply each equation to get one of the variables to drop out.

Add the equations.

(-15q)=(-9990)

q=666

1000-666=334

There are 666 quarters and 334 dimes.

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Q: You have 1000 coins to make 199.90 how many dimes and quarters?
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