You have ten fewer quarters than dimes and 5 fewer nickles than quarters. The total value of the coins is $4.75. How many quarters, nickles, and dimes do you have?

0.05n + 0.10d + 0.25q = 4.75

d = q + 10

n = q - 5

0.05 (q - 5) + 0.10 (q + 10) + 0.25q = 4.75

0.05q - 0.25 + 0.10q + 1 + 0.25q = 4.75

0.40q + 0.75 = 4.75

0.40q = 4.75 - 0.75

0.40q = 4

q = 4 / 0.40

q = 10 < = = = quarters

d = q + 10

d = 10 + 10

d = 20 < = = dimes

n = q - 5

n = 10 - 5

n = 5 < = = nickels

Q=d-10, n=q-5, Solve the first for d and you have:

d=q+10 and n=q-5

.25q+.1d+.05n=4.75, then using d and n from above, this becomes:

.25q+.1 (q+10) +.05 (q-5) = 4.75 perform indicated multiplications

.25q+.1q+1+.05q-.25=4.75 combine like terms

.4q+.75=4.75 subtract. 75 from both sides

.4q=4 divide both sides by. 4

q=10, since d=q+10 and n=q-5

d=20, n=5

So you have 10 quarters, 20 dimes, and 5 nickels.