Let L = Lace Ribbon and S = Satin Ribbon.
1st customer: 3L + 2S = 120 yards.
2nd customer: 2L + 4S = 160 yards.
Multiply the 1st customer equation by -2:
-6L + -4S = -240
Add the 2 equations together:
-6L + 2L = -4L
-4S +4S = 0S
-240 + 160 = -80
So now you have -4L = -80
Divide both sides by -4 to find the quantity of L:
L = -80 / -4
L = 20 yards.
Each roll of Lace has 20 yards.
Now replace L with 20 in the original equation for the first customer to solve for S:
3L + 2S = 120 yards.
3(20) + 2S = 120
60 +2S = 120
Subtract 60 from each side:
2S = 60
Divide both sides by 2 to solve for S
S = 60/2
S = 30 yards
There is 20 yards per roll of Lace and 30 yards per roll of satin.
The answer is the first one.
