Question

Heath wants 10 L of a solution that is 90% bleach. He will combine pure bleach with a mixture that is 20% bleach.

(a) Write a system of equations to model the problem. Use p for the number of liters of pure bleach and m for the number of liters of the mixture that is 20% bleach.

(b)Solve the system. Show your work. How many liters of pure bleach will Heath use? How many liters of the 20% mixture will he use?

Answer 1

We need 10 liters of 90% bleach.
We have pure bleach (p) and 20% bleach (m)
A) p + m = 10 liters
B) p + .2m = (.90 * 10)
multiplying equation B by -1
B) -p - .2m = -9 then adding equation A
A) p + m = 10

.8 m =1
m = 1.25 liters of 20% bleach
p = 8.75 liters of 100% bleach

Double Check
The 1.25 liters of 20% bleach contains .25 liters of pure bleach.
Basically, we have (8.75 liters + .25 liters) 9 liters of pure bleach in a volume of 10 liters. 9 / 10 = .9 equals 90%