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 40 coins, all of them dimes and quarters. when she added them up, she had a total of $7.75. how many dimes did jenna have

Let Q= the number of quarters and D= the number of dimes.
Q+D= 40 coins
0.25Q+0.1D= $7.75
Rewrite equation 1 as: D = 40-Q and substitute into equation 2
0.25Q+0.1(40-Q)= 7.75 Simplify the left side
0.25Q+4-0.1Q= 7.75 Subtract 4 from both sides
0.25Q-0.1Q= 3.75 Convime like terms on left side
0.15Q= 7.75 Divide both sides by 0.15
Q=25 and D= 40-Q
D= 40-25 which is 15
So Jenna had 25 quarters and 15 dimes.
To check multiply 25 x 25 and 15x10 which equals 625 and 150 this equals 775 so this is 7.75

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