Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 70% pure fruit juice, and the second type is 95% pure fruit juice. How many pints of each drink must be used to make 50 pints of a mixture that is 90% pure fruit juice?

Answer 1

`10` of the `70%` pure fruit juice, `40` of the `95%` pure fruit juice.

Explanation:

This is a system of equations question.

First, we define our variables: let `x` be the number of pints of the first fruit drink (`70%` pure fruit juice), and `y` be the number of pints of the second fruit drink (`95%` pure fruit juice).

We know that there are `50` total pints of the mixture. Thus:

`x+y=50`

We also know that `90%` of those `50` pints will be pure fruit juice, and all of the pure fruit juice will come from `x` or `y`.

For `x` pints of the first juice, there is `.7x` pure fruit juice. Similarly, for `y` pints of the first juice, there is `.95y` pure fruit juice. Thus, we get:

`.7x+.95y=50*.9`

Now we solve. First I'll get rid of the decimals in the second equation by multiplying by `100`:

`70x+95y=4500`

Multiply the first equation by `70` on both sides to be able to cancel out one of the terms:

`70x+70y=3500`

Subtract the second equation from the first equation:

`25y=1000`

`y=40`

Thus, we need `40` pints of the second fruit juice (`95%` pure fruit juice). This means that we need `50-40=10` pints of the first fruit juice (`70%` pure fruit juice).