Sarah K. answered • 03/28/19
Tutor for the SAT for over 10 years
If the total of quarters (q) plus nickels (n) equals 87 coins, equation #1 can be:
q + n = 87
Let's isolate one variable, say n, and solve for it.
n = 87 - q
Equation #2 wants us to find out how many of each coin do we have so that they total to $12.55.
A quarter is 25% ($0.25) of a dollar ($1) and a nickel is 5% ($0.05) of a dollar ($1). Why is this important? Because the units of 12.55 are in dollars ($) and we have to relate our variables to that.
Therefore equation #2 is:
0.25q + 0.05n = 12.55
We know that n = 87 - q from equation #1 so let's plug that in to solve for q (number of quarters).
0.25q + 0.05n = 12.55 where n = 87 - q
0.25q + 0.05(87 - q) = 12.55
0.25q + 4.35 - 0.05q = 12.55
0.25q - 0.05q = 12.55 - 4.35
0.20q = 8.2
q = 41 (we have 41 quarters)
Let's double check and look at equation #1. If we have 41 quarters, and total coins are 87, then the number of nickels must be 87 - 41 = 46.
Double check one more time for equation #2. If we have 41 quarters and 46 nickels, do they total to $12.55?
41(0.25) + 46(0.05) = 10.25 + 2.3 = 12.55, yes.
You have 41 quarters and 46 nickels.
