How many cups of grapefruit juice must be added to 60 cups of a punch that is 6% grapefruit juice to obtain a punch that is 10% grapefruit juice?
Amount (in cups):

Question

How many cups of grapefruit juice must be added to 60 cups of a punch that is 6% grapefruit juice to obtain a punch that is 10% grapefruit juice? Amount (in cups):

SnapAndSolve AI · Accepted Answer

Let x be the amount of grapefruit juice to be added.

The initial amount of grapefruit juice in the punch is 6% of 60 cups, which is 0.06 * 60 = 3.6 cups.

After adding x cups of pure grapefruit juice, the total amount of grapefruit juice becomes 3.6 + x cups.

The total volume of the punch becomes 60 + x cups.

We want the final concentration to be 10%, so:

(3.6 + x) / (60 + x) = 0.10

Solving for x:

3.6 + x = 0.10 * (60 + x)
3.6 + x = 6 + 0.10x
3.6 + x - 0.10x = 6
3.6 + 0.90x = 6
0.90x = 6 - 3.6
0.90x = 2.4
x = 2.4 / 0.90
x = 2.67

2.67 cups of grapefruit juice must be added.

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How many cups of grapefruit juice must be added to 60 cups of a punch that is 6% grapefruit juice to obtain...

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