Problem Solving

BTGmoderatorDC wrote: ↑

Tue Oct 06, 2020 7:12 pm

A drum of bathroom cleaner contains 200 gallons of a cleaning solution that is 20% bleach. If 50 gallons of water are added to the solution, what percent of the new solution is composed of bleach?

A. 12%
B. 15%
C. 16%
D. 18%
E. 20%


OA C

Solution:

Initially there are 200 x 0.2 = 40 gallons of bleach in the solution. After 50 gallons of water are added to the solution, there are 250 gallons of solution, but there are still 40 gallons of bleach. Therefore, the percent of the new solution that is composed of bleach is:

40/250 = 4/25 = 16/100 = 16%

Alternate Solution:

To 200 gallons of 20% bleach we add 50 gallons of water, which is 0% bleach. The result is 250 gallons of (100x)% bleach. We can express this in an equation as follows:

200(0.20) + 50(0.0) = 250x

40 + 0 = 250x

4/25 = x

0.16 = x

The percent of bleach of the new solution is 16%.

Answer: C