Question

Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution. The equation 0.10x + 0.15(50 – x) = 0.12(50) can be used to find the amount of 10% alcohol solution Bruce should use.

How much of the 10% alcohol solution should Bruce use?

mL

How much of the 15% alcohol solution should Bruce use?

mL

1. The amount of the 10% alcohol solution  that Bruce should use is 30ml and the amount of the 15% alcohol solution  that Bruce should use is 20ml.

### Alcohol solution

Given:
Equation 0.10x + 0.15(50 – x) = 0.12(50)
Let x represent  10% alcohol solution that Bruce should use
Hence:
0.10x + 0.15(50 – x) = 0.12(50)
0.10x + 7.5-0.15x=6
Collect like term
0.10x-0.15x=6-7.5
-0.05x=-1.5
Divide both side by -0.05x
x=-1.5/-0.05
x=30 ml
b. 15% alcohol solution
(50 – x), when x=30 ml
(50-30)
=20 ml
Therefore the amount of the 10% alcohol solution  that Bruce should use is 30ml and the amount of the 15% alcohol solution  that Bruce should use is 20ml.
2. 