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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

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 produ class=

Respuesta :

First fruit drink with 45% concentration will contain 14 pints

Second fruit drink with 70% concentration will contain 56 pints

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

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