A beverage company mixes a beverage that contains 10 fruit j

A beverage company mixes a beverage that contains 10% fruit juice with another one that contains 50% fruit juice. How many gallons of each should they mix to obtain 1300 gallons of a mix that contains 40% fruit juice? First set up a system of equations for this problem and then solve the system.

Solution

Let x gallons of the 1^st beverage containing 10 % fruit juice be mixed with y gallons of the 2^nd beverage containing 50 % fruit juice to obtain 1300 gallons of a beverage containing 40 % fruit juice . Then we have x +y = 1300…(1) ( this equates the quantity of beverage on both the sides) and x*0.1 +y*0.5 = 1300*0.4 ( this equates the quantity of juice on both the sides). On multiplying both the sides by 10, we get x +5y = 5200…(2). Then, on subtracting the 1^st equation from the 2^nd equation ( to eliminate x), we get x+5y –(x+y) = 5200-1300 or, 4y = 3900 so that y = 3900/4 = 975. Now, on substituting y = 975 in the 1^st equation, we get x+975 = 1300 so that x = 1300-975 = 325. Thus, 325 gallons of the 1^st beverage containing 10 % fruit juice be mixed with 975 gallons of the 2^nd beverage containing 50 % fruit juice to obtain 1300 gallons of a beverage containing 40 % fruit juice . We can verify the result by substituting x = 325 and y = 975 in the 2^nd equation.