17 adam has $2.15 in nickels, dimes and quarters in his pocket. if the number of dimes is 4 less than the number of nickels, and 5 more than the number of quarters, then how many of each type of coin does he have?

12 nickels, 8 dimes, 3 quarters

Step-by-step explanation:

    Nickels     + Dimes +  Quarters   = Total

0.20 + 0.05d + 0.10d + 0.25d - 1.25 = 2.15

                                       0.40d - 1.05 = 2.15

                                       0.40d           = 3.20

                                               d            = 8

Nickels: 4 + d   = 4 + (8)   = 12

Quarters: d - 5   = (8) - 5   = 3

Check:

Nickels:   0.05(12)  = $0.60

Dimes:     0.10 (8)   = $0.80

Quarters: 0.25(3)   = $0.75

                Total:     = $2.15  

there are infinitely many solutions.