SOLUTION: 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)

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Question 1156281: 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
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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..., make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution.
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If want x of the 10% alcohol, then use 50-x of the 15% alcohol.

Accounting for quantities of alcohol to give the expected amount of pure alcohol: 0.10x%2B0.15%2850-x%29=0.12%2A50;

0.1x%2B0.15%2A50-0.15x=0.12%2A50
%280.1-0.15%29x=0.12%2A50-0.15%2A50
%280.15-0.1%29x=0.15%2A50-0.12%2A50
highlight%28x=50%28%280.15-0.12%29%2F%280.15-0.1%29%29%29, and you can finish this.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

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?
How much of the 15% alcohol solution should Bruce use?
0.10x + 0.15(50  -  x) = 0.12(50)

The given equation indicates that the 10% solution was named x

This means that the 15% solution is 50 - x,  as named

.1x + .15(50 - x) = .12(50)

.1x + 7.5 - .15x = 6

.1x - .15x = 6 - 7.5

- .05x = - 1.5

x, or amount of 10% solution to mix = highlight_green%28matrix%281%2C4%2C+%28-+1.5%29%2F%28-+.05%29%2C+%22=%22%2C+30%2C+mL%29%29

Now, can you find the amount of 15% solution to mix?