Question

A change drawer contains $7.50 made up entirely of quarters, nickels, and dimes. There are twice as many nickels as dimes, and the number of dimes and quarters sum to 34. Determine the number of nickels, dimes, and quarters in the drawer.

Answer 1

There are 40 nickels, 14 quarters and 20 dimes.

Explanation:

A change drawer contains $7.50

Let the number of quarters in the drawer = q

let the number of nickels in the drawer = n

and number of dimes = d

So, (0.25q + 0.05n + 0.10d) = 7.5

By dividing the equation by 0.50

5q + n + 2d = 150 ---------(1)

Now statement says " There are twice as nickels as dimes"

n = 2d -------(2)

And "the number of dimes and quarters sum to 34"

d + q = 34 -------(3)

We replace n = 2d from equation (2) in equation (1)

5q + 2d + 2d = 150

5q + 4d = 150 ---------(4)

Multiply equation (3) by 4 and subtract it from equation (4)

(5q + 4d) - 4(d + q) = 150 - 34×4

5q - 4q + 4d - 4d = 150 - 136

q = 14

We plug in the value of q in equation (3)

d + 14 = 34

d = 34 - 14

d = 20

Since n = 2d

So n = 2×20

n = 40

Therefore, there are 40 nickels, 14 quarters and 20 dimes.

Answer 2

The drawer contains 40 nickels, 20 dimes and 14 quarters.

Explanation:

Let d, q and n represent number of dimes, quarters and nickels respectively.

We have been given that there are twice as many nickels as dimes.

`n=2d...(1)`

Further, the number of dimes and quarters sum to 34.

`d+q=34...(2)`

As the change drawer contains $7.50 made up entirely of quarters, nickels, and dimes.

`0.10d+0.25q+0.05n=7.50...(3)`

From equation (2), we will get:

`q=34-d`

Substituting equation (1) and equation (2) in equation (3), we will get:

`0.10d+0.25(34-d)+0.05(2d)=7.50`

`0.10d+8.50-0.25d+0.10d=7.50`

`-0.05d+8.50=7.50`

`-0.05d+8.50-8.50=7.50-8.50`

`-0.05d=-1`

`(-0.05d)/(-0.05)=(-1)/(-0.05)`

`d=20`

Therefore, drawer contains 20 dimes.

Substitute
`d=20` in equation (1):

`n=2d`

`n=2(20)`

`n=40`

Therefore, drawer contains 40 nickels.

Substitute
`d=20` in equation (2):

`20+q=34`

`20-20+q=34-20`

`q=14`

Therefore, drawer contains 14 quarters.