Question 343440
Liza has 60 coins in her collection. The coin collection consists of nickles, dimes and quarters. She has five fewer quarters than nickles and ten more dimes than quarters. How many coins of each kind does Liza have?  Thank you. 



let N = number of nickles, D = number of dimes, Q = number of quarters
N + D + Q = 60
Q = N - 5 (5 fewer quarters than nickels)
D = Q + 10 (10 more dimes than quarters)
D = N - 5 + 10 (substituted for Q)
D = N + 5 (simplified)
N + N + 5 + N - 5 = 60 (substituted in Q and D)
3N = 60 (simplified)
N = 20 nickles


Q = N - 5 = 20 - 5 = 15 quarters


D = N + 5 = 20 + 5 = 25 dimes


check:
N + D + Q = 20 + 25 + 15 = 45 + 15 = 60 coins (as wanted)
Q = N - 5 = 20 - 5 = 15 quarters (checked)
D = Q + 10 = 15 + 10 = 25 dimes (checked)