Pete wants to mix 4 quarts of 20% orange juice concentrate with some 60% pineapple juice concentrate to get a 50% punch concentrate for a party. How much of the 60% pineapple juice concentrate should be used? Pete wants to mix 4 quarts of 20% orange juice concentrate with some 60% pineapple juice concentrate to get a 50% punch concentrate for a party. How much of the 60% pineapple juice concentrate should be used?

Pete starts with 4 quarts of 20% juice, which contains

0.20 • (4 quarts) = 0.8 quarts

of juice.

If he mixes this with x quarts of 60% juice, which contains

0.60 • (x quarts) = 0.6x quarts

of juice, then he would end up with a mixture with a volume of (x + 4) quarts that contains (0.8 + 0.6x) quarts of juice. The mix has to have a concentration of 50% juice, which means

(0.8 + 0.6x) / (x + 4) = 0.50

Solve for x :

0.8 + 0.6x = 0.50 (x + 4)

0.8 + 0.6x = 0.5x + 2

0.1x = 1.2

x = 12

So Pete needs 12 quarts of the 60% juice.

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8