Math fruit company

Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 30% pure fruit juice, and the second type is 55% pure fruit juice. The company is attempting to produce a fruit drink that contains 40% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 180 pints of a mixture that is 40% pure fruit juice? 

Answer 1

Let FJ30 = pints of the 30% fruit juice

FJ55 = pints of the 50% fruit juice

then,

FJ30 + FJ55 = 180

and (30*FJ30 + 55*FJ55)/(FJ30 + FJ55) = 40 or (30*FJ30 + 55*FJ55) = 40(180) = 7,200

so FJ30 + FJ55 = 180 or 30*FJ30 + 30*FJ55 = 5,400

and 30*FJ30 + 55*FJ55 = 7,200 and 30*FJ30 + 55*FJ55 = 7,200

Subtracting, we have

25*FJ55 = 1,800

or FJ55 = 72 (pints of the 55% juice)

and FJ30 = 180 - 72 = 108 (pints of the 30% juice)