## Pola​ Sommers, a massage​ therapist, needs 44 ounces of a 2020​% lavender oil solution. She has only 55​% and 3030​% lavender oil solutions

Question

Pola​ Sommers, a massage​ therapist, needs 44 ounces of a 2020​% lavender oil solution. She has only 55​% and 3030​% lavender oil solutions available. How many ounces of each should Pola mix to obtain the desired​ solution?

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3 weeks 2021-10-08T01:16:52+00:00 1 Answer 0

1. Answer: 2.4 ounces of the 30% solution and 1.6 ounces of the 5% solution.

Step-by-step explanation: Every number is written two times.

Pola needs 4 ounces of 20% lavender oil solution, and she has only 5% and 30% oil solutions, so she needs to mix them.

If X is the number of ounces of 5% solution, and Y is the number of ounces of the 30% solution, we have that:

X + Y = 4

(X*0.05 + Y*0.30)/(X + Y) = 0.20

Where I used the percentages in the decimal form because the math is easier.

From the first equation, we can isolate one of the variables, and replace it in the other.

X = 4 – Y

((4-Y)*0.05 + Y*0.30)/(4 – Y + Y) = 0.20

(4*0.05 + Y*(0.25))/4 = 0.20

Y*0.25 = 0.8 – 0.20 = 0.60

Y = 0.60/0.25 = 2.4

So she needs to use 2.4 ounces of the 30% solution, and the other 1.6 ounces are from the 5% solution.