How many pints of each of the two existing types of drink must be used to make 120 pints of a mixture that is 65% pure fruit juice?

Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 45%

 pure fruit juice, and the second type is 70%

 pure fruit juice. The company is attempting to produce a fruit drink that contains 65%

 pure fruit juice. How many pints of each of the two existing types of drink must be used to make 120

 pints of a mixture that is 65%

 pure fruit juice?

Answer 1

This is a mixture problem. The trick is to think in terms of h.m. pure fruit juice there is in the various drink solutions.

Assume A pints of mixture A at 45% concentration. So the amt of pure juice is 0.45A

For B, the amt of pure juice is 0.70B for B pints.

The final mixture is 120 pts at 65%, that contains 0.65 x 120 = 78 pints of pure juice.

0.45A + 0.70 B = 78 but B = 120 - A

0.45A + 0.7(120 - A) = 78 -> 0.45A + 84 - 0.7A = 78 -> -0.25A = -6 -> A = 6/0.25 = 24 pts. of mixture A

So need use 120 - 24 = 96 pts. for mixture B.

Check: 0.45 x 24 = 10.8 pts of pure jc.

0.70 x 96 = 67.2 pts of pure jc.

Total 78 pts pure juice in 120 pts of mixture. 78/120 = 65% (OK)