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?

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:

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

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:

               +

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

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Step-by-step explanation: