Solving a percent mixture problem

Question

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 90% salt. She wants to obtain 130 ounces of a mixture that is 85% salt. How many ounces of each solution should she use?

Answer 1

This is a mixture problem that can be solved by setting up a system of equations.  There are a couple pieces of important information here.  The first is that we want to obtain a 130 ounce mixture so the amount of solution A and B have to add up to 130:

 

(1)  A + B = 130

 

The second is that the amount of salt in the final mixture should be 85% salt or:

 

85% x 130 ounces = 110.5 ounces of salt

 

Since solution A is 65% salt and B is 90% we know that:

 

(2)  A x 65% + B x 90% = 110.5

 

From (1), A = 130 - B by subtracting B from both sides.  We can substitute this into (2) to get:

 

(3)  (130 - B) x 65% + B x 90% = 110.5

 

Now all that is left is simplifying the equation above and solving for B:

 

130 x 65% - B x 65% + B x 90% = 110.5 

84.5 + B x 25 % = 110.5

B x 25% = 26

B = 104

 

And from (1) we have A = 130 - B = 26.