Question 499299
To solve mixture problems, you have to determine how much "pure" stuff you have and how much you need in the final mix.
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You have 40 cups of 2% grapefruit juice.
40*.02 = .8 cup of pure grapefruit juice, or 8/10 of a cup.
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You have an unlimited supply of 100% grapefruit juice that you have to mix with the 2% to obtain a final amount of juice mixture that is 10% grapefruit juice.
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Looking at this logically, if you had 10% juice, you would have to have 4 cups of pure juice in the 40 cups of punch.  But, everything you add increases the volume, so you have to model it.
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x = amount of pure juice to add
40+x = amount of 10% punch you will have in the end.
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Pure grapefruit juice in the final produce = 10%*(40+x).
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Your ingredients are:
2%*40 + 100%*x = 10%*(40+x)
.02*40 + x = .1(40+x)
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Multiply by 100 to remove percents
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2*40 + 100x = 10(40+x)
80 + 100x = 400 + 10x
90x = 320
x = 320/90
x = 32/9 cups
x = 3 5/9 cups to add to the 40 cups you have
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Check your answer by determining how much pure stuff you have vs. how much you ought to have.
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You have 43 5/9 cups of total mix.
= 43.555 cups
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You have 8/10 + 32/9 cups of pure stuff.
 = 4.3555 cups
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So, the final mixture is indeed 10% grapefruit juice.
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Answer:
Add 3 5/9 cups of pure grapefruit juice.