You are making 6 quarts of juice. You have bottles of 100% juice and bottles of 80% juice. How many quarts of each type of juice should you mix to make 6 quarts of 80% juice?

Question

This question can be solved using systems of linear equations. We should make the equations and then decide if we want to use substitution or elimination to solve for one of the variables. Then we can solve for the other variable.

Answer 1

We have a total of 6 quarts. We need to know how many of each kind to make 6 quarts of 80% juice.

x = 100% juice

y= 20% juice

x+y=6 quarts of 80% juice

We also know we need 6 quarts of 80% juice combining 20% and 100% juice.

1x + .20y = .80

Sometimes working with decimals is more challenging so lets change this equation to be whole numbers. I can multiply everything in this equation by 100 and get whole numbers. As long as I multiply each piece by 100, I have followed the math rules.

100(1x+.20y=80

100x+20y=80

Now I can solve the system of equations by elimination or substitution.

100x+20y=100

x+y=6 ** I choose to multiply this equation by -20

100x+20y=100

-20x-20y=-120 now subtract the two equations

80x=120

x=1.5

Substitute x into the first equations

1.5+y=6

y=4.5

We will need 1.5 gallons of 20% juice and 4.5 gallons of 100% juice to make 6 gallons of 80% juice,