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?

Answer:First type of fruit drinks: 48 pintsSecond type of fruit drinks: 32 pintsStep-by-step explanation:Let's call A the amount of first type of fruit drinks. 55% pure fruit juiceLet's call B the amount of second type of fruit drinks. 80% pure fruit juiceThe 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]