algebra word problem

Question

Ted's bill for 6 cans of grape juice and 4 cans of orange juice was $13.20. When he got home, he found that he should have bought 4 cans of grape juice and 6 cans of orange juice. Though he mixed up the order, he did save 60 cents. How much does each can cost?

Answer 1

You can set up a system of equations based on the information they gave you.

g will stand for grape juice; o will stand for orange juice

6g + 4o = 13.20

4g = 6o = 13.80

Now you just need to solve the system of equations!

We can multiply the first equation by 2 and the second by 3.

12g + 8o = 26.40

12g + 18o = 41.40

Eliminating the 12g through subtraction leaves us with: -10o = -15

After solving for o, we get that a can of orange juice costs $1.50

We can then substitute that into one of the original equations to get 6g + 4(1.50)=13.20

Simplify:

6g + 6 = 13.20

6g = 7.20

g=1.20

So, a can of grape juice costs $1.20