Question

Matt wants to make a 25% alcohol solution. He has already poured 1.5 qt. of pure water into a beaker. How many qt. of a 30% alcohol solution must he add to this to create the desired mixture?

A. 3 qt.
B. 4.5 qt.
C. 6 qt.
D. 7.5 qt.

Answer 1

To create a 25% alcohol solution, Matt must add 7.5 qt. of a 30% alcohol solution to 1.5 qt. of pure water.

Step-by-step explanation:

To solve this problem, we can set up an equation using the concept of concentration. Let's say Matt needs to add x qt. of the 30% alcohol solution. The amount of alcohol in the water is 0 qt., and the amount of alcohol in the 30% solution is 0.3x qt. The total amount of alcohol in the desired mixture is 0.25(1.5 + x) qt. Since the total amount of alcohol should equal the sum of the alcohol in the water and the 30% solution, we can set up the equation:

0.25(1.5 + x) = 0 + 0.3x

To solve for x, we can distribute the 0.25 and then combine like terms:

0.375 + 0.25x = 0.3x

Next, subtract 0.25x from both sides:

0.375 = 0.05x

Divide both sides by 0.05:

x = 7.5

Therefore, Matt must add 7.5 qt. of the 30% alcohol solution to create the desired mixture.