Solve a system of linear equations, and solve word problems by modeling them with a system of linear equations.

Question

If a nurse has two alcohol solutions, the first (A), a 30% alcohol solution, and the second (B), a 60% alcohol solution, but needs 10 liters of a 40% alcohol solution, how much of each of these two solutions (A & B) is needed?

Answer 1

Thanks for your question. What you would want to do is set up an equation like this:

x + (10-x) = 10 L

Let x be your solution A and let 10-x be your solution b. Solution b is 10-x because we know that the amount we need of solution b can be determined after determining how much of solution a we need. We know that in the end we need 1000 mLs of a . 40% alcohol solution so:

0.30x + 0.60(10-x)= 0.40 (10)

0.30x + (6-0.60x)= 4

Now subtract the 6 from both sides

0.30x-0.60x = -2

-0.30x = - 2

You would then want to divide each side by -0.30

-0.30x/-0.30 = -2/-0.30

x = 6.67L

So now you would go back through your equation and determine that x (which is solution a) would require 6.67 L and solution b (10-x) requires 3.33 L to make a 10L 40% solution.

I hope this helps.

Stephanie