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.