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Serga [27]
3 years ago
14

Pete wants to mix 4 quarts of 20% orange juice concentrate with some 60% pineapple juice concentrate to get a 50% punch concentr

ate 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?
Mathematics
1 answer:
Tamiku [17]3 years ago
7 0

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

0.20 • (4 quarts) = 0.8 quarts

of juice.

If he mixes this with <em>x</em> quarts of 60% juice, which contains

0.60 • (<em>x</em> quarts) = 0.6<em>x</em> quarts

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

(0.8 + 0.6<em>x</em>) / (<em>x</em> + 4) = 0.50

Solve for <em>x</em> :

0.8 + 0.6<em>x</em> = 0.50 (<em>x</em> + 4)

0.8 + 0.6<em>x</em> = 0.5<em>x</em> + 2

0.1<em>x</em> = 1.2

<em>x</em> = 12

So Pete needs 12 quarts of the 60% juice.

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