There are some nickels, dimes, and quarters in a large piggy bank. for every 2 nickels there 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.

Let the equation be: n + d + q = 500 let this be 1

n/2 = d/3 (for every 2 nickels there are 3 dimes) let this be 2

d/2 = q/5 (for every 2 dimes, there are 5 quarters) let this be 3

from 2, n = 2/3d

from 3, q = 5/2d

substitute the given values into equation 1:

2/3d + d + 5/2d = 500

Multiply by 6 both sides

4d + 6d + 15d = 3000

25d = 3000

d = 3000/25

d = 120

120 dimes, 2/3 x 120 = 80 nickels and 5/2 x 120 = 300 quarters.

259 nickels, 172 dimes and 69 quarters are present in the piggy bank.

According to the question, for every 2 nickels there dimes and for every 2 dimes there are 5 quarters.

and,

And, a total number of coins in the piggy bank is 500.

So,

Substitute in ,

Again,

Substitute in ,

,

Hence, 259 nickels, 172 dimes and 69 quartersare present in the piggy bank.

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