Question

A scientist needs 4.8 liters of a 12% alcohol solution. She has available a 22% and a 10% solution. How many liters of the 22% and how many liters of the 10% solutions should she mix to make the 12% solution?

Liters of 10% solution =


Liters of 22% solution =

pls someone help!!

Answer 1

• 4.0 L of 10%
• 0.8 L of 22%

Explanation:

For mixture problems, it is convenient to define a variable to represent the amount of the greatest contributor. Let x represent the amount of 22% solution in the mix. Then 4.8-x is the amount of 10% solution.

The amount of alcohol in the mix is ...

0.22x +0.10(4.8-x) = 0.12(4.8)

Eliminating parentheses, we have ...

0.22x -0.10x +0.10(4.8) = 0.12(4.8)

Subtracting (0.10)(4.8) and combining x-terms gives ...

0.12x = 0.02(4.8)

x = (0.02/0.12)(4.8) = 0.8 . . . . . divide by the x-coefficient

The scientist needs 0.8 L of 22% solution and 4.0 L of 10% solution.