Question

Joey has a full 40 coins consisting of only quarters and nickels if the total value is $5.00 how many of each does joey have.

Answer 1

n=number of nickles
q=number of quarters

40 coins total so
n+q=40

total value is 500 cents
5n+25q=500
divide both sides by 5
n+5q=100


so we gots
n+q=40
n+5q=100

elimination
multily first equation by -1 and add to 2nd equation

-n-q=-40
n+5q=100 +
0n+4q=60

4q=60
divide both sides by 4
q=15

sub back
n+q=40
n+15=40
minus 15 both sides
n=25


25 nickles and 15 quarters

Answer 2

q + n = 40....q = 40 - n
0.25q + 0.05n = 5

0.25(40 - n) + 0.05n = 5
10 - 0.25n + 0.05n = 5
-0.25n + 0.05n = 5 - 10
- 0.20n = -5
n = -5 / -0.20
n = 25 <=== 25 nickels

q + n = 40
q + 25 = 40
q = 40 - 25
q = 15 <== 15 quarters