Question

How many gallons of 9% peroxide solution must be mixed with 3 gallons of a 15% peroxide solution to obtain a 12% solution?

a) 2.5 gallons
b) 3.5 gallons
c) 4.5 gallons
d) 5.5 gallons

Answer 1

To obtain a 12% peroxide solution by mixing a 9% solution with a 15% solution, you must mix equal parts of each. Specifically, you would need 3 gallons of the 9% solution to mix with 3 gallons of the 15% solution.

Step-by-step explanation:

To determine how many gallons of 9% peroxide solution must be mixed with 3 gallons of a 15% peroxide solution to obtain a 12% solution, we can use the method of weighted averages. Let x represent the gallons of 9% solution needed.

We set up the equation based on the concept that the total amount of peroxide in the mixed solutions must be equal to the amount in the final solution:

1. (0.09)x + (0.15)(3) = (0.12)(x + 3)
2. 0.09x + 0.45 = 0.12x + 0.36
3. Subtract 0.09x from both sides: 0.45 = 0.03x + 0.36
4. Subtract 0.36 from both sides: 0.09 = 0.03x
5. Divide both sides by 0.03 to find x: x = 3

Therefore, 3 gallons of 9% peroxide solution are needed to create a 12% peroxide solution when mixed with 3 gallons of a 15% peroxide solution.