Question

Solve the problem by setting up and solving a system of three linear equations in three variables. a box contains $7.20 n nickels, dimes, and quarters. there are 42 coins in all, and the sum of the numbers of nickels and dimes is 2 less than the number of quarters. how many coins of each kind are there

Answer 1

n+d+q=42
n+d=q-2
q-2+q=42
2q=44
q=22
n+d=20

5n+10d+25q=720
n+2d+5q=144
n+2d+110=144
n+2d=34
n=-d+20
-d+20+2d=34
d=14
n=6

There are 22 quarters, 14 dimes, and 6 nickles.