Question

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 70% salt and Solution B is 95% salt. She wants to obtain 150 ounces of a mixture that is 75% salt. How many ounces of each solution should she use?

Answer 1

Solution A: 120 ounces

Solution B: 30 ounces

Explanation:

Let's call A the amount of Solution A. Solution A is 70% salt

Let's call B the amount of Solution B. Solution A is 95% salt

The resulting mixture should have 75% salt and 150 ounces .

Then we know that the total amount of mixture will be:

`A + B = 150`

Then the total amount of salt in the mixture will be:

`0.7A + 0.95B = 0.75 * 150`

`0.7A + 0.95B = 112.5`

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.95 and add it to the second equation:

`-0.95A -0.95B = 150 * (-0.95)`

`-0.95A -0.95B =-142.5`

`-0.95A -0.95B =-142.5`

+

`0.7A + 0.95B = 112.5`

--------------------------------------

`-0.25A = -30`

`A = (-30)/(-0.25)`

`A = 120\ ounces`

We substitute the value of A into one of the two equations and solve for B.

`120 + B = 150`

`B = 30\ ounces`