SOLUTION: 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 man

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.
Found 2 solutions by solver91311, CharlesG2:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let represent the number of nickels.

Let represent the number of dimes.

Let represent the number of quarters.

And we know:

But we also know that

and

but that means:

Then substituting:

Solve for and then the other two values follow directly.

John

My calculator said it, I believe it, that settles it

Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
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)

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