Question

A jar contains quarters and nickels. There are 5 fewer quarters than nickels. The

total value of the coins is $4.45. Which system of equations can be used to
determine the number of quarters, q, and the number of nickels, n?

Answer 1

Given:

In a jar, there are 5 fewer quarters than nickels.

The total value of the coins is $4.45.

To find:

The system of equations can be used to determine the number of quarters, q, and the number of nickels, n.

Solution:

Let q be the number of quarters and n be the number of nickels.

It is given that there are 5 fewer quarters than nickels.

`q=n-5` ...(i)

We know that,

1 quarter = $0.25

1 nickel = $0.05

Using these conversions, we get

q quarters = $0.25q

n nickels = $0.05n

The total value of the coins is $4.45.

`0.25q+0.05n=4.45` ...(ii)

The equations (i) and (ii) are equations of required system of equations.

Therefore, the system of equations is:

`q=n-5`

`0.25q+0.05n=4.45`