Sam has a total of 43 quarters and nickels in her purse. If her change is worth $7.75, how many nickels and how many quarters does Sam have? Warning: This is Algebra 1

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.