The Piggy Bank

You have 100 coins totaling $5.00. They consist of pennies, dimes, and half dollars. How many of each are there?

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Let P be the number of pennies, D the number of dimes, and H the number of half dollars. P + D + H = 100 and P + 10D + 50H = 500, so 9D + 49H = 400. Now, we know that H is less than 10, and the only value for which (400 – 49H) is divisible by 9 is 1. So the totals are 1 half dollar, 39 dimes, and 60 pennies. “If you take care of your peonies,” wrote Franklin P. Adams, “the dahlias will look after themselves.”