Question

Garrett's coin bank contains 500 nickels,

dimes, and quarters. He has the same
number of nickels as dimes, and the total
value of the coins is $72.50. How many
quarters does he have?

Answer 1

Explanation:

d = number of dimes

n = number of nickels

q = number of quarters

d + n + q = 500

d×$0.10 + n×$0.05 + q×$0.25 = $72.50

n = d

we are focusing now on one variable (let's try d), and we are transforming the other equations to express the other variable by this one variable.

since n = d we have already

d + d + q = 500

2d + q = 500

q = 500 - 2d

with that we go into the main equation

d×0.10 + d×0.05 + (500 - 2d)×0.25 = 72.50

d×0.15 + (500 - 2d)×0.25 = 72.50

d×0.15 + 500×0.25 - 2d×0.25 = 72.50

d×0.15 + 125 - d×0.50 = 72.50

-d×0.35 = -52.50

d = 52.50/0.35 = 150

n = d = 150

q = 500 - 2d = 500 - 2×150 = 500 - 300 = 200

so, he has 200 quarters.