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 15% alcohol solution should Bruce use?

Answer 1

(50 - x) is the amount of the 15% Alcohol solution to use. If you solve for x first.
0.10x + 0.15(50 – x) = 0.12(50)
0.10x - 0.15x + 7.5 = 6
-0.05x + 7.5 = 6
7.5 - 6 = 0.05x
1.5 = 0.05x
1.5/0.05 = x
30 mL = x

Then the 15% solution: 50 - 30 = 20 mL

Answer 2

The amount of 15% alcohol Bruce should use ls 20 mL

Using the equation given in the question :

0.10x + 0.15(50 - x) = 0.12(50)

0.10x + 7.5 - 0.15x = 6

Collect like terms

-0.05 = 6 - 7.5

-0.05x = - 1.5

x = 1.5 / 0.05

x = 30 mL

The amount of 15% solution to be used is related can be calculated thus :

Amount of 15% solution = 50 - x

Amount of 15% solution = 50 - 30 = 20mL

Therefore, 20mL of 15% solution is required.

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