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The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 65%
pure fruit juice?

Respuesta :

luisejr77

Answer:

First type of fruit drinks: 48 pints

Second type of fruit drinks: 32 pints

Step-by-step explanation:

Let's call A the amount of first type of fruit drinks. 55% pure fruit juice

Let's call B the amount of second type of fruit drinks. 80% pure fruit juice

The resulting mixture should have 65% pure fruit juice and 80 pints.

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

[tex]A + B = 80[/tex]

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

[tex]0.55A + 0.8B = 0.65 * 80[/tex]

[tex]0.55A + 0.8B = 52[/tex]

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.8 and add it to the second equation:

[tex]-0.8A -0.8B = -0.8*80[/tex]

[tex]-0.8A -0.8B = -64[/tex]

[tex]-0.8A -0.8B = -64[/tex]

               +

[tex]0.55A + 0.8B = 52[/tex]

--------------------------------------

[tex]-0.25A = -12[/tex]

[tex]A = \frac{-12}{-0.25}[/tex]

[tex]A = 48\ pints[/tex]

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

[tex]48 + B = 80[/tex]

[tex]B = 32\ pints[/tex]

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