For every 2 nickels there are 3 dimes. For every 2 dimes there are 5 quarters. There are 500 coins in total. How many nickels, dimes, and quarters are in the piggy bank? Explain your reasoning.

80 nickels 120 dimes 300 quarters

Step-by-step explanation:

The ratio of nickels to dimes is 2 : 3 = 4 : 6.

The ratio of dimes to quarters is 2 : 5 = 6 : 15.

Then the ratios of nickels : dimes : quarters are ...

4 : 6 : 15

There are a total of 4+6+15 = 25 ratio units representing 500 coins, so each one represents 500/25 = 20 coins. Then the numbers of coins are ...

nickels : dimes : quarters = 4·20 : 6·20 : 15·20 = 80 : 120 : 300

There are 80 nickels, 120 dimes, and 300 quarters in the piggy bank.