Every evening jenna emptied her pocket and put your change in a jar at the end of the week she counts her money one week she had 40 coins all of the them dimes and quarters then she added them up she had a total of $7.75

Jenna had 25 quarters and 15 dimes.

Step-by-step explanation:

Let Q = the number of quarters and D = the number of dimes.

Then:

1) Q+D = 40 "One week she had 40 coins, all of them dimes and quarters"

2) 0.25Q+0.1D = $7.75 "...she had a total of $7.75."

Rewrite equation 1) as: D = 40-Q and substitute into equation 2).

2a) 0.25Q+0.1(40-Q) = 7.75 Simplify the left side.

2b) 0.25Q+4-0.1Q = $7.75 Subtract 4 from both sides.

2c) 0.25Q-0.1Q = 3.75 Combine the like-terms on the left side.

2d) 0.15Q = 7.75 Divide both sides by 0.15

2e) Q = 25 and:

D = 40-Q

D = 40-25

D = 15

Jenna had 25 quarters and 15 dimes.