The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 100% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 240 pints of a mixture that is 70%
pure fruit juice?

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luisejr77 luisejr77 · Answer 1 · 2019-06-11T19:33:25+02:00

Answer:

First type of fruit drinks: 160 pints

Second type of fruit drinks: 80 pints

Step-by-step explanation:

Let's call A the amount of first type of fruit drinks. 5.5% pure fruit juice

Let's call B the amount of second type of fruit drinks. 100% pure fruit juice

The resulting mixture should have 70% pure fruit juice and 240 pints.

Then we know that the total amount of mixture will be:

[tex]A + B = 240[/tex]

Then the total amount of pure fruit juice in the mixture will be:

[tex]0.55A + B = 0.7 * 240[/tex]

[tex]0.55A + B = 168[/tex]

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -1 and add it to the second equation:

[tex]-A -B = -240[/tex]

+

[tex]0.55A + B = 168[/tex]

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[tex]-0.45A = -72[/tex]

[tex]A = \frac{-72}{-0.45}[/tex]

[tex]A = 160\ pints[/tex]

We substitute the value of A into one of the two equations and solve for B.

[tex]160 + B = 240[/tex]

[tex]B = 80\ pints[/tex]