Question

A collection of coins consists of nickels, dimes, and quarters. There are four fewer quarters than nickels and 3 more dimes and quarters. How many of each kind of coin are in the collection if the total value of the collection is $6.5?

Answer 1

Let's start the problem by assigning variables to the unknown quantities. Let's call the number of nickels "n", the number of dimes "d", and the number of quarters "q".

From the problem, we know:

- q = n - 4 (there are four fewer quarters than nickels)
- d + q = q + 3 (there are 3 more dimes than quarters)
- The total value of the collection is $6.5

To convert everything to cents, we can multiply everything by 100:

- 5n + 10d + 25q = 650 (total value in cents)

Now, we can use the first two equations to get rid of one variable.

Substituting q in terms of n:

- q = n - 4

Substituting q in terms of d:

- q = d + 3

Since both equations are equal to q, they must be