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?

1 Answer
Oct 15, 2017

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).