SOLUTION: Use two equations in two variables to solve the application. See Example 6. (Objective 1) A chemist has one solution that is 40% alcohol and another that is 55% alcohol. How muc

Algebra ->  Finance -> SOLUTION: Use two equations in two variables to solve the application. See Example 6. (Objective 1) A chemist has one solution that is 40% alcohol and another that is 55% alcohol. How muc      Log On


   

Question 1164916: Use two equations in two variables to solve the application. See Example 6. (Objective 1)
A chemist has one solution that is 40% alcohol and another that is 55% alcohol. How much of each must she use to make 15 liters of a solution that is 50% alcohol?
40% solution
L
55% solution
L
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
You already saw solutions to examples like this done in two variables and two unknowns. Here is what you could do to keep as just one single variable.

v liters of the 55%
15-v liters of the 40%
55v%2B40%2815-v%29=50%2A15
and solve for v, but simplify LATER.

55v%2B40%2A15-40v=50%2A15
55v-40v=50%2A15-40%2A15
%2855-40%29v=15%2850-40%29
highlight_green%28v=15%28%2850-40%29%2F%2855-40%29%29%29-------Think why this form is shown before simplifying it; and then computing v. Then, evaluate 15-v.

You could do the solution as two equations and unknowns if you really want to.