How many pints of each of the two existing types of drink must be used to make pints of a mixture that is pure fruit juice?

Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 30%

 pure fruit juice, and the second type is 80%

 pure fruit juice. The company is attempting to produce a fruit drink that contains 40%

 pure fruit juice.



Answer 1

30X+80X =40(100) = 4000

30(100-Y) +80Y = 4000

3000 -30Y +80Y = 4000

50Y = 1000

Y = 20 pints of 80%

X= 100-20 = 80 pints of 30%

If you wanted 100 pints of 55% pure fruit juice then

you'd want equal amounts of each, as 30+80 divided by 2 = 55, but you want 40% which is closer to 30 than 80, so you want more of the 30 than the 80

30X + 80Y = 55(100), where X = 30% and Y=80%

and

X +Y = 100

or

X = 100-Y

and

30(100-Y) +80Y = 5500

3000-30Y +80Y = 5500

50Y = 2500

Y = 2500/50 = 50 pints of 80%

X=100-50=50 pints of 30%