Shelley has a collection of dimes, nickels and quarters that is worth $5.25. There are a total of 48 coins. If there are 7 more nickels than quarters, how many dimes are there?

25 dimes

Step-by-step explanation:

Given

Coins: Nickels (N), Quarters (Q) , and Dimes (D)

$0.05 = 1 nickel, $0.10 = 1 dime  and $0.25 = 1 quarter

So, the amount implies:

The number of coin implies:

and

Required

Determine the number of Dimes

Substitute 7 + Q for N in the first and second equation

Collect Like Terms

----- (1)

Collect Like Terms

Make Q the subject

Substitute 20.5 - 0.50D for Q in  (1)

Solve for D

Hence, there are 25 Dimes