Sam Squeeze has 10 quarts of a drink that is 60% organge juice. how much pure orange juice must he add to get a drink that is 75% orange juice?

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To solve this problem, we can set up an equation based on the given information and use algebra to find the answer.

Let's assume that Sam wants to add x quarts of pure orange juice.

Currently, Sam has 10 quarts of a drink that is 60% orange juice. This means that 60% of the 10 quarts is actually orange juice, or 0.6 * 10 = 6 quarts.

After adding x quarts of pure orange juice, the total volume of the mixture will be 10 + x quarts. The amount of pure orange juice in the mixture will be the sum of the original amount (6 quarts) and the amount added (x quarts).

So, the amount of pure orange juice in the mixture will be 6 + x quarts.

To get a drink that is 75% orange juice, the amount of pure orange juice must be 75% of the total volume of the mixture. This can be expressed as 0.75 * (10 + x) quarts.

Now we can set up an equation:

6 + x = 0.75 * (10 + x)

Simplifying the equation:

6 + x = 7.5 + 0.75x

Rearranging the terms:

0.25x = 1.5

Dividing both sides by 0.25:

x = 6

Therefore, Sam needs to add 6 quarts of pure orange juice to get a drink that is 75% orange juice.