Alan has twice as many dimes as he has quarters and 10 more nickels than dimes. The remaining 35 coins are pennies. How many of quarters, dimes and nickels does he have if he has $2.50?

He has 3 quarters, 6 dimes and 16 nickles

Step-by-step explanation:

∵ Dimes is d, Quarter is q, nickels is n and pennies is p

∵ Quarter = 25 cents

∵ Dime = 10 cents

∵ Nickle = 5 cents

∵ Penny = 1 cent

∵ The remaining 35 coins are pennies ⇒ 35 cents

∵ He has $2.50 = 2.50 * 100 = 250 cents

∴ The value of quarters, dimes and nickels = 250 - 35 = 215 cents

∴ 25q + 10d + 5n = 215 ⇒ (1)

∵ d = 2q

∴ q = 1/2d ⇒ (2)

∵ n = 10 + d ⇒ (3)

Substitute (2) and (3) in (1)

∴ 25 (1/2 d) + 10d + 5 (10 + d) = 215

∴ 12.5d + 10d + 50 + 5d = 215

∴ 27.5d = 215 - 50

∴ 27.5d = 165

∴ d = 165 : 27.5

∴ d = 6

∴ q = 1/2 (6) = 3

∴ n = 10 + 6 = 16

∴ He has 3 quarters, 6 dimes and 16 nickles

3 quarters, 6 dimes, and, 16 nickels