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).