Bill, a health food enthusiast, is mixing concoctions in his basement. He's invented a new drink that needs to be 40% carrot juice and 60% other stuff. He has been to the store and has found some concentrated carrot juice (60% carrot juice). His neighbor Clara, who decided one day that she doesn't like carrot juice that much anymore, has contributed 80 quarts of 12% carrot juice. How many quarts of the concentrated carrot juice does he need to add to the 80 quarts of weak juice to produce his perfect drink with 40% carrot juice

Question

Mathematics

Atticus Marks

30 August, 02:38

Bill, a health food enthusiast, is mixing concoctions in his basement. He's invented a new drink that needs to be 40% carrot juice and 60% other stuff. He has been to the store and has found some concentrated carrot juice (60% carrot juice). His neighbor Clara, who decided one day that she doesn't like carrot juice that much anymore, has contributed 80 quarts of 12% carrot juice. How many quarts of the concentrated carrot juice does he need to add to the 80 quarts of weak juice to produce his perfect drink with 40% carrot juice

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Twinkie · Answer 1

112

Step-by-step explanation:

We have to:

x is the number of quarts of 60% juice required.

We also know that pure carrot juice in 60% juice (0.6 * x) added to the amount of pure carrot juice in 12% juice 9.6 (0.12 * 80) has to be equal to the amount of carrot juice pure in the final mixture (0.4 * (80 + x)).

Therefore numerically it is the following:

0.6 * x + 9.6 = 0.4 * (80 + x)

Solving for x, we are left with:

0.6 * x + 9.6 = 32 + 0.4 * x

0.6 * x-0.4 * x = 32-9.6

0.2 * x = 22.4

x = 22.4 / 0.2

x = 112

That is, 112 quarts of 60% juice are required.