Math CentralQuandaries & Queries


Question from danielle, a parent:

In changing a $5 bill, Sarah received nine more dimes than nickels and seven fewer quarters than dimes. How many coins of each type did she receive?


I can help get you started. Let N be the number of nickels, D the number of dimes and Q he number of quarters. A nickel is worth 5 cents, a dime 10 cents, a quarter 25 cents and a five five dollar bill 500 cents. Thus

5N + 10D + 25Q = 500.

You can divide both sides of this equation by 5 to simplify it and obtain

N + 2D + 5Q = 100.

There are two more statements "Sarah received nine more dimes than nickels" and "Sarah received seven fewer quarters than dimes". Write these two statements as equations using N, D and Q and solve the three equations.

If you still have difficulty solving this show me what you did and I will try to help some more.


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