Nick has 31 coins, make up of quarters, nickels, and dimes. if he had one more dime, he would have just as many dimes as he has nickels and quarters put together. if the total value of nick’s coins is $4.70, how many coins of each does he have?

Q + d + n = 31n + q = 31 - d
0.25q + 0.10d + 0.05n = 4.7
d + 1 = (n + q)

31 - d = d + 1
31 - 1 = d + d
30 = 2d
30/2 = d
15 = d

(n + q) = d + 1
n + q = 16
n = 16 - q

0.25q + 0.10d + 0.05n = 4.70
0.25q + 0.10(15) + 0.05(16 - q) = 4.70
0.25q + 1.50 + 0.80 - 0.05q = 4.70
0.20q + 2.30 = 4.70
0.20q = 4.70 - 2.30
0.20q = 2.40
q = 2.40/.20
q = 12

n = 16 - q
n = 16 - 12
n = 4

Nick has : 12 quarters, 15 dimes, and 4 nickels