Question

a scientist has two solutions which she has labeled solutions A and Solution B each contains salt she knows that solutions A is 30% salt and solution B is 80% salt. she wants to obtain 120 ounces of a mixture that is 60% salt how many ounces of each solution should she use

Answer 1

Explanation:

Let's call A the ounces of solution A and B the ounces of solution B.

If the scientist wants to obtain 120 ounces, then:

A + B = 120

On the other hand, the final mixture should be 60% salt and solution A is 30% salt and solution B is 80% salt, so:

0.6(A + B) = 0.3A + 0.8B

So, we can solve for A as:

$\begin{gathered} 0.6(A+B)=0.3A+0.8B_{}_{} \\ 0.6A+0.6B=0.3A+0.8B \\ 0.6A+0.6B-0.3A=0.3A+0.8B-0.3B \\ 0.3A+0.6B=0.8B \\ 0.3A+0.6B-0.6B=0.8B-0.6B \\ 0.3A=0.2B \\ \frac{0.3A}{0.3}=\frac{0.2B}{0.3} \\ A=\frac{2}{3}B \end{gathered}$

Then, replacing A by (2/3)B on the first equation, we get:

$\begin{gathered} A+B=120 \\ \frac{2}{3}B+B=120 \\ \frac{5}{3}B=120 \\ 3\cdot\frac{5}{3}B=3\cdot120 \\ 5B=360 \\ \frac{5B}{5}=\frac{360}{5} \\ B=72 \end{gathered}$

Finally, A is equal to:

$\begin{gathered} A=\frac{2}{3}B \\ A=\frac{2}{3}(72) \\ A=48 \end{gathered}$

Therefore, she should use 48o

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