a chemist needs to make 3o ounces of a 30% alcohol solution by mixing a 15% alcohol solution with a 40% alcohol solution. how many ounces of the 40% solution does she need

Question

a chemist needs to make 3o ounces of a 30% alcohol solution by mixing a 15% alcohol solution with a 40% alcohol solution. how many ounces of  the 40% solution does she need

hero · Answer

We don't know how many ounces of solution are in the 15% alcohol solution or the 40% alcohol solution, but we do know that after mixing, there will be 30 ounces of solution so we can create this equation to represent the situation

x + y = 30

where 
x = amount of ounces in the 15% solution
y = amount of ounces in the 40% solution

anonymous · Answer

so like 10 and 20?

hero · Answer

Hang on...we can't just guess the amounts.

hero · Answer

Whatever amount of x ounces is in the first solution, 15% of it will be alcohol.
Whatever amount of y ounces in the second solution, 40% of it will be alcohol.

After combining the amounts there will be 30% of 30 ounces of solution. 

We can represent this by the following equation
.15x + .40y = .30(30)

hero · Answer

So we can setup and solve this system of equations:

     x + y = 30
.15x + .40y = 9

hero · Answer

It is best that if you have any questions, please ask so that any confusion may be clarified.