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.

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

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