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Q: My piggy bank contains only nickels, dimes, and quarters, and contains 20 coins worth a total of $3.30. If the total value of the quarters is five times the total value of all the other coins, how many dimes are in the piggy bank?

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My piggy bank contains only nickels, dimes, and quarters, and contains 20 coins worth a total of $3.30. If the total value of the quarters is five times the total value of all the other coins, how many dimes are in the piggy bank?
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If the quarters are 5 times the amount of the other coins, then that means there are 6 units (5 in quarters, 1 in everything else). If you divide 3.30 by 6, you get 55 cents per unit. 5 times 55 cents gets you 2.75, which is the value of the quarters. That means 55 cents is left available for nickels and dimes.

55 cents in nickels and dimes can have many forms. 5 dimes and 1 nickels; 4 dimes and 3 nickels, 3 dimes and 5 nickels, etc, all the way to no dimes and 11 nickels.

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