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
Answer:
She had 17 dims and 21 quarters to make $6.95.
Step-by-step 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. [tex]d+q=38[/tex] ......(1)
The value of d is 0.10 and q is 0.25.
The total she had of $6.95
i.e. [tex]0.10d+0.25q=6.95[/tex] .......(2)
Solving (1) and (2),
Substitute d from (1) into (2)
[tex]0.10(38-q)+0.25q=6.95[/tex]
[tex]0.10\times 38-0.10q+0.25q=6.95[/tex]
[tex]3.8+0.15q=6.95[/tex]
[tex]0.15q=6.95-3.8[/tex]
[tex]0.15q=3.15[/tex]
[tex]q=\frac{3.15}{0.15}[/tex]
[tex]q=21[/tex]
Substitute in equation (1),
[tex]d+21=38[/tex]
[tex]d=38-21[/tex]
[tex]d=17[/tex]
Therefore, She had 17 dims and 21 quarters to make $6.95.
