Math CentralQuandaries & Queries


Question from Alexandra, a student:

Ellen has two more nickels than dimes and three more quarters than nickels. She has $3.35 in all. How many coins of each type does she have?

Hi Alexandra,

You could use guess-and-check for this problem. Let's say my guess is that I have $3.00 in quarters, that's 12 quarters. That would mean 9 nickels (three more quarters than nickels) and 7 dimes (two more nickels than dimes). This would give a value of

0.25 x 12 + 0.05 x 9 + 0.10 x 7 = $300 + $0.45 + $0.90 = $4.35.

This is too much. Since quarters are worth the most I must have too many quarters so refine the guess to fewer quarters and continue.

A better method would be to use algebra. The two statements two more nickels than dimes and three more quarters than nickels each involve nickels so I am going to let the number of nickels be the variable.

Let N be the number of nickels then the number of dimes in N - 2 and the number of quarters is N + 3. Thus the amount of money Ellen has in nickels is

$0.05 N

Find the amount of money she has in dimes and quarters and add the three quantities. The sum must be $3.35 which gives you an equation in N which you can solve.

I hope this helps,

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