Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 20% pure fruit juice, and the second type is 95% pure 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 used to make 70 pints of a mixture that is 80% pure fruit juice?

Answer 1

14 pints of 20% pure fruit juice and 56 pints of 95% pure fruit juice be used to make 70 pints of a mixture that is 80% pure fruit juice

Explanation:

Let the volume of 20% pure fruit juice be x pints

Let the volume of 95% pure fruit juice be y pints

Total volume drink company desires to make = 70 pints

x + y = 70 ...[1]

Volume of Juice in 20% pure fruit juice = 20% of x = 0.2x pints

Volume of Juice in 95% pure fruit juice = 95% of y = 0.95y pints

Volume of fruit juice in 70 pints = 80% of 70 pints = 0.08 × 70 pints

0.2x pints + 0.95y pints = 0.08 × 70 pints

4x + 19y = 1,120....[2]

On solving [1] and [2] we get:

x = 14 pints , y = 56 pints

14 pints of 20% pure fruit juice and 56 pints of 95% pure fruit juice be used to make 70 pints of a mixture that is 80% pure fruit juice

Answer 2

14 pints of 20% juice

56 pints of 95% juice

Explanation:

Let

x be pints of 20% pure fruit juice, thus

70 - x will be pints of 95% pure fruit juice

The equation, thus can be written as:

20%x + 95% (70-x) = 80% (70)

Solving for x:

`(0.2)x + (0.95)(70-x) = (0.8)(70)\\0.2x+66.5-0.95x=56\\0.75x=10.5\\x=14`

And 70 - x would be 70 - 14 = 56

Thus,

14 pints of 20% juice is needed, and

56 pints of 95% juice is needed