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How many cups of a drink with 10% fruit juice should Taylor mix with 6 cups of 100% fruit juice to make a drink that is 25% fruit juice?

a. 4 cups
b. 5 cups
c. 6 cups
d. 7 cups

User Statement
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1 Answer

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Final answer:

Taylor needs to mix 5 cups of a drink with 10% fruit juice with 6 cups of 100% fruit juice to make a drink that is 25% fruit juice. The correct answer is option b. 5 cups.

Step-by-step explanation:

The correct answer is option b. 5 cups.

To solve this, we'll set up an equation where x represents the number of cups with 10% fruit juice. We have 6 cups of 100% fruit juice and we want the final mixture to be 25% fruit juice. We can create the following equation:

0.10x + 1(6) = 0.25(x + 6)

Now, solve for x:

0.10x + 6 = 0.25x + 1.5

0.25x - 0.10x = 6 - 1.5

0.15x = 4.5

x = 4.5 / 0.15

x = 30 / 1.5

x = 5 cups

Taylor needs to mix 5 cups of a drink with 10% fruit juice to achieve a 25% fruit juice concentration when mixed with 6 cups of 100% fruit juice.

To find the number of cups of the 10% fruit juice, let's set up a proportion.

Let x be the number of cups of the 10% fruit juice.

So, we have the proportion:

10%/100% = x/(6 + x)

Cross multiplying, we get:

10% * (6 + x) = 100% * x

Simplifying, we have:

0.1(6 + x) = x

Expanding the equation, we get:

0.6 + 0.1x = x

Subtracting 0.1x from both sides, we get:

0.6 = 0.9x

Dividing both sides by 0.9, we find:

x = 0.6/0.9 = 0.67

So, Taylor should mix 0.67 cups of the 10% fruit juice with 6 cups of the 100% fruit juice to make a drink that is 25% fruit juice.

User MattSavage
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