Let q= the number of quarters
Let n=the number of nickels
q+n=43 This equations represents the total number of coins.
0.25q+0.05n=7.75 This equations represents her change totaling to $7.75.
Multiply the second equation by 100 to simplify the arithmetic.
q+n=43
25q+5n=775 Multiply the first equation by -5.
-5q-5n=-215
25q+5n=775 Add the two equation in which the n variable gets eliminated.
20q=560 Divide both sides by 20.
q=28 Substitute q=28 into the first equation and solve for n.
28+n=43
-28 -28
n=15 Therefore, she has 28 quarters and 15 nickels in her purse.
Hope this helps.