Question

How many gallons of pure water should be added to 10 gallons of a soultion containing 15% juice so that the remaining solution contains 5% juice?

A. 1.5
B. 10
C. 0
D. X

Answer 1

To dilute a 15% juice solution to a 5% juice solution, you must add 20 gallons of pure water to the original 10 gallons of the solution.

Step-by-step explanation:

To determine how many gallons of pure water should be added to 10 gallons of a 15% juice solution to dilute it to a 5% juice solution, we use the concept of the concentration of solutions. The amount of pure water added will dilute the juice percentage in the original solution.

We start with 10 gallons of 15% juice, which means that there is 1.5 gallons of juice in the original solution. If we add x gallons of water, the total volume of the new solution will be (10 + x) gallons, and it will still contain the original 1.5 gallons of juice. We want this 1.5 gallons of juice to represent 5% of the total solution volume.

The equation representing this situation is 1.5 / (10 + x) = 0.05, because 5% is equal to 0.05 as a decimal. Solving for x gives:

1.5 = 0.05(10 + x)

1.5 = 0.5 + 0.05x

1.0 = 0.05x
x = 20

Therefore, to achieve a 5% juice solution, you would need to add 20 gallons of pure water to the original solution.