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.