Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 45% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 75% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 110 pints of a mixture that is 75% pure fruit juice? First fruit drink=Second fruit drink=

Answer 1

First fruit juice of 45% = 44 pints

Second fruit juice of 95% = 66 pints

Step-by-step explanation:

let the pints for the 45% pure fruit = x

let the pints for the 95% pure fruit juice = y

Total pints = 110

% for the 110 pints = 75%

x + y = 110 ...equation 1

x(45%) + y(95%) = 110(75%)

x(0.45) + y(0.95) = 110(0.75)

0.45x + 0.95y = 82.5 ...equation 2

Using substitution method:

From equation 1, x = 110 - y

substitute for x in equation 2:

0.45(110 - y) + 0.95y = 82.5

49.5 - 0.45y + 0.95y = 82.5

49.5 + 0.5y = 82.5

0.5y = 82.5 - 49.5

0.5y = 33

Divide through by 48.55:

y = 33/0.5 = 66

substitute for y in equation 1:

x + 66 = 110

x = 44

First fruit juice of 45% = 44 pints

Second fruit juice of 95% = 66 pints