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CEMC Gauss (Grade 7), 2015

Algebra Difficulty 1.6 Junior Find the answer Canada

You have exactly $4.40 (440 ¢) in quarters (25 ¢ coins), dimes (10 ¢ coins), and nickels (5 ¢ coins). You have the same number of each type of coin. How many dimes do you have?

Pick one

Solution

The total value of one quarter, one dime and one nickel is $25+10+5=40$ ¢.

Since you have equal numbers of quarters, dimes and nickels, you can separate your coins into piles, each containing exactly 1 quarter, 1 dime, and 1 nickel.

Each pile has a value of 40¢, and since $440\div40=11$ , then you must have 11 quarters, 11 dimes and 11 nickels.

Therefore, you have 11 dimes.
Note: You can check that $11\times(25$ ¢ $\,+ 10$ ¢ $\,+5$ ¢ $)=11\times40$ ¢ $=440$ ¢ $=\$4.40$ , as required.

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