nickels and dimes

Question

There are 60 nickels, dimes, and quarters totaling $7,20.  If there are five times as many quarters as dimes, how many nickels are there?

Answer 1

n + d + q = 60

5n + 10d + 25q = 720

q = 5d

 

If we multiply the first equation by 5 and subtract the second equation from it...

 

5n + 5d + 5q = 300

5n + 10d + 25q = 720

 

-5d - 20q = -420

5d + 20q = 420

 

5d + 20(5d) = 420

5d + 100d = 420

105d = 420

d = 4

 

q = 5(4)

q = 20

 

n + 4 + 20 = 60

n + 24 = 60

n = 36