Question

Every evening Jenna empties her pockets and puts her change in a jar. At the end of the week she counts her money. One week she had 38 coins all of them dimes and quarters. When she added them up she had a total of $6.95

Answer 1

She had 17 dims and 21 quarters to make $6.95.

Explanation:

Given : Every evening Jenna empties her pockets and puts her change in a jar. At the end of the week she counts her money. One week she had 38 coins all of them dimes and quarters.

To find : When she added them up she had a total of $6.95?

Solution :

Let d be the dims and q be the quarters.

She had 38 coins.

i.e.
`d+q=38` ......(1)

The value of d is 0.10 and q is 0.25.

The total she had of $6.95

i.e.
`0.10d+0.25q=6.95` .......(2)

Solving (1) and (2),

Substitute d from (1) into (2)

`0.10(38-q)+0.25q=6.95`

`0.10* 38-0.10q+0.25q=6.95`

`3.8+0.15q=6.95`

`0.15q=6.95-3.8`

`0.15q=3.15`

`q=(3.15)/(0.15)`

`q=21`

Substitute in equation (1),

`d+21=38`

`d=38-21`

`d=17`

Therefore, She had 17 dims and 21 quarters to make $6.95.

Answer 2

d = dimes

q = quarters

d+q = 38 coins

q=38-d

0.25q + 0.10d=6.95

0.25(38-d)+0.10d=6.95

9.5-0.25d+0.10d=6.95

-015d=-2.55

d=-2.55/-0.15 = 17

q=38-17 =21

21*0.25 =5.25

17*0.10 = 1.70

5.25+1.70 = 6.95

she had 21 quarters and 17 dimes