Question

Jasmine wants to make a 30% alcohol solution. She

has already poured 3 fluid ounces of a 72% alcohol
solution into a beaker. How many fluid ounces of a 9%
alcohol solution must she add to create this desired
mixture?

Answer 1

It will be equal to 180

Answer 2

Jasmine needs to add 6 fluid ounces of the 9% alcohol solution to her 3 fluid ounces of 72% alcohol solution in order to create a 30% alcohol solution mixture. This was determined by setting up a mixture equation and solving for x, which represents the volume of the 9% alcohol solution needed.

Step-by-step explanation:

To solve Jasmine's problem using a mixture equation, you need to set up an equation based on the total amount of pure alcohol in the final solution. We denote the final volume of the 9% alcohol solution needed as 'x' ounces. The amount of alcohol in the original 72% solution is 3 ounces × 0.72, and the amount of alcohol in the 9% solution is x × 0.09. The total volume of the final solution will be 3 + x ounces, and the total amount of alcohol in the final solution should be 0.30 × (3 + x) ounces, because Jasmine wants a 30% alcohol solution. The mixture equation will therefore be:

3 × 0.72 + x × 0.09 = 0.30 × (3 + x)

This simplifies to:

2.16 + 0.09x = 0.90 + 0.30x

Rearranging terms to solve for x gives:

0.21x = 1.26

x = 6 ounces

Thus, Jasmine needs to add 6 fluid ounces of the 9% alcohol solution to the 3 fluid ounces of 72% alcohol solution to make the desired 30% solution mixture.