A pile of coins, consisting of nickels, dimes, and quarters, is worth $4.55. There are 4 more dimes than nickels and 3 quarters more than dimes. How many of each are there?

let: number of nickels = n then: number of dimes = n+4 and: number of quarters = (n+4) + 3 = n+7 express total amount in cents $4.55 = 455 cents express total in cents by multiplying quantities of coins by value and adding them up. 455 = 5*n + 10 * (n+4) + 25 * (n+7) 455 = 5n + 10n + 40 + 25n + 175 240 = 40n n = 6 so number of nickels = 6. number of dimes = number of nickels + 4 = 6+4 = 10 number of quarters = number of dimes + 3 = 10+3 = 13 There are 6 nickels, 10 dimes and 13 quarters.