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?

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%