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?

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We need 50 ml of a 12% alcohol solution.
We have 10% and 15% alcohol solutions and we want 50 ml at 12%
We set up 2 equations (x is volume of 10% y is volume of 15%)

a) x + y = 50
b) .1x + .15y = 6.0 (which is 50 ml at 12% or .12 * 50)

multiplying equation "a" by -.1 then add it to "b"
a) -.1x -.1y = -5
b) .1x +.15y = 6.0

.05y = 1
y = 20 ml of 15% and therefore x would equal 30 ml of 10%

Cdoes not have two variables