Dan opened up his piggy bank and found a total of thirty-five coins, made up of nickels, dimes, and quarters. if he has five more nickels than dimes and a total of $6, how many of each coin were in his bank?

N + d + q = 35
0.05n + 0.10d + 0.25q = 6
n = d + 5

n + d + q = 35
0.05n + 0.10d + 0.25q = 6multiply by -4

n + d + q = 35
-0.20n - 0.40d - q = - 24 (result of multiplying by -4)
add
0.80n + 0.60d = 11

0.80(d + 5) + 0.60d = 11
0.80d + 4 + 0.60d = 11
1.40d = 11 - 4
1.40d = 7
d = 7 / 1.40
d = 5 < there are 5 dimes

n = d + 5
n = 5 + 5
n = 10 < there are 10 nickels

n + d + q = 35
10 + 5 + q = 35
15 + q = 35
q = 35 - 15
q = 20 <=== there are 20 quarters