Question

A vending machine has $50.40 in it. There are 432 coins total and the machine only accepts nickels and quarters. How many nickels and quarters are in the machine?​

Answer 1

Nickels = n
Quarters = q

n + q = 432

Nickels are 5 cents (0.05)
Quarters are 25 cents (0.25)

0.05n + 0.25q = 50.40

Use substitution or elimination (I like substitution)
n + q = 432 means n = 432 - q

So 0.05n + 0.25q = 50.4 is
0.05(432 - q) + 0.25q = 50.4
21.6 - 0.05q + 0.25q = 50.4
21.6 + 0.2q = 50.4
0.2q = 28.8
q = 144

Plug in to find nickels
n + q = 432 means
n + 144 = 432
n = 288