Piggy bank problem

Question

There are some nickels, dimes, and quarters in a large piggy bank. For every 2 nickels there are 3 dimes. For every 2 dimes there are 5 quarters. There are 500 coins total.

a. How many nickels, dimes, and quarters are in the piggy bank? Explain your reasoning.

b. How much are the coins in the piggy bank worth?

Answer 1

n + d + q= 500 coins

n + d + 5d/2 = 500

n + 7d/2 = 500

n = 500-7d/2

2/5 = d/q for every 2 dimes there are 5 quarters, it's a 2/5 ratio = d/q

5d = 2q

q = 5d/2

5n +10d +25q = total value

3rd restriction is n,d,q are integers

so that

total value = 115(.05) +110(.10) + 275(.25) = $83 in the piggy bank

with 275 quarters

110 dimes

and 115 nickels

for every 2 dimes there are 5 quarters

2/5 = d/q = 110/275 = .4

115 + 110 + 275 = 500 coins