How much of​ a(n) orange juice drink must be mixed with gallons of a orange juice drink to obtain a mixture that is orange​ juice?

Question

How much of​ a(n)

60%

orange juice drink must be mixed with

8

gallons of a

40%

orange juice drink to obtain a mixture that is

50%

orange​ juice?

Answer 1

This one can be done by observing that 50% is exactly halfway between 40% and 60%. Therefore, to get a 50% mixture you'd need an equal amount of each. Since there are 8 gals of the 40% mixture, you'd need 8 gals of the 60% mixture as well.

Here's the algebra:

x = gal of 60% juice. Focus on how much pure orange juice there is in each of the mixtures and how much total volume you'll have once they're mixed.

0.60x + 0.40(8) = 0.50(x + 8)

0.60x + 3.2 = 0.50x + 4

0.10x = 0.8

x = 8 gals