The Royal Fruit Company produces two types of fruit drinks. The first type is 70% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 80% pure fruit juice. How many pints of each of the two existing types of drink must be posed
to make 60 pints of a mixture that is 80% pure fruit juice?
First fruit drink = pints?
Second fruit drink=pints?

Let x = amount of 70% juice we use.

Then 60-x = amount of 85% juice we'll use.

We'll set up an equation that is based on how much pure juice comes from each component and how much we need in the final mixture.

So 70% of x plus 85% of (60-x) must equal 80% of 60, or...

    0.7x + 0.85(60-x) = 0.8(60)

    0.7x + 51 - 0.85x = 48

    -0.15x + 51 = 48

    -0.15x = -3

     x = 20

Then 60 - x = 60 - 20 = 40

Check: 70% of 20 pints = 14 pints of pure juice.

            85% of 40 pints = 34 pints of pure juice

            That's 48 pints of pure juice in the mix, which matche 80% 0f 60 pints.

You'd need 20 pints of the 70% juice and 40 pints of the 85% juice.