Question

Audio fruit company produces two types of food drinks prototype in 45% pure fruit juice and the second time is 70% pure fruit juice company is attempting to produce a fruit fruit drink take the time to 65% pure fruit juice how many pints of each other to existing types of drinks must be used to make 70 pints make sure to 65% pure juice

Answer 1

First fruit drink with 45% concentration will contain 14 pints

Second fruit drink with 70% concentration will contain 56 pints

Step-by-step explanation:

Let the amount fruit juice contiaining 45% = x

let the amount of fruit juice containing 70% = y

The percentage of the mixture = 65%

Amount of fruit juice in the mixture = 70 pints

This means x + y will give 70 pints

x + y = 70 ....(1)

The concentration of each of the fruit juice:

45%(amount) + 70% (amount) = 65% (70)

45%(x) + 70%(y) = 65% (70)

0.45(x) + 0.7(y) = 0.65(70)

0.45x + 0.7y = 45.5 ....(2)

combining both equations:

x + y = 70 ....(1)

0.45x + 0.7y = 45.5 ....(2)

Using substitution method:

from equation (1), we can make x the subject of formula

x = 70 - y

substitute for x in equation (2):

0.45(70 - y) + 0.7y = 45.5

31.5 - 0.45y + 0.7y = 45.5

31.5 + 0.25y = 45.5

collect like terms:

0.25y = 45.5 - 31.5

0.25y = 14

divide both sides by 0.25:

y = 14/0.25

y = 56

Substitute for y in equation (1):

x + 56 = 70

x = 70 - 56

x = 14

First fruit drink with 45% concentration will contain 14 pints

Second fruit drink with 70% concentration will contain 56 pints