A collection of 108 coins containing only quarters and nickels is worth $21 how many quarters are there

N = number of nickels

q = number of quarters

equation 1: n+q=108

equation 2:.05n+.25q=21

Want to solve for q, so multiply by 20 to equation 2.

20 (.05n+.25q=21) = 1n+5q=420

Subtract equation 2 from equation 1.

n-n+q-5q=108-420

-4q=-312 Divide by - 4 to both sides to get

q=78.

108 - n = q (q is how many quarters there are)