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?

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.

18.75 gallons

step-by-step explanation:

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus