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?

Answer:First type of fruit drinks: 160 pintsSecond type of fruit drinks: 80 pintsStep-by-step explanation:Let's call A the amount of first type of fruit drinks. 5.5% pure fruit juiceLet's call B the amount of second type of fruit drinks. 100% pure fruit juiceThe 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]-A -B = -240[/tex]                   +[tex]0.55A + B = 168[/tex]--------------------------------------[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]