you have 95 coins that total $10.75. the coins consist of only quarters and nickels. how many of each coin do you have?

Answer 1

.25q+.05n=10.75 (1)
q+n=95 (2)
Multiply (2) by -.25 to cancel the q's
.25q+.05n=10.75 (1)
-.25q-.25n=-23.75 (3)
-.2n=-13
Divide both sides by -.2
n=65
From (2), q+n=95, q+65=95, q=30
When plugged back into equation 1, it checks. It works in both equations, so this is your solution.

Answer 2

You have a total of $175 in $5 and $20 bills. The number of $5 bills you have is 3 more than 4 times the number of $20 bills. How many of each type of bill do you have?