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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?

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luisejr77

Answer:

Solution A: 120 ounces

Solution B: 30 ounces

Step-by-step 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:

[tex]A + B = 150[/tex]

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

[tex]0.7A + 0.95B = 0.75 * 150[/tex]

[tex]0.7A + 0.95B = 112.5[/tex]

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:

[tex]-0.95A -0.95B = 150 * (-0.95)[/tex]

[tex]-0.95A -0.95B =-142.5[/tex]

[tex]-0.95A -0.95B =-142.5[/tex]

                      +

[tex]0.7A + 0.95B = 112.5[/tex]

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

[tex]-0.25A = -30[/tex]

[tex]A = \frac{-30}{-0.25}[/tex]

[tex]A = 120\ ounces[/tex]

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

[tex]120 + B = 150[/tex]

[tex]B = 30\ ounces[/tex]

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