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

Step-by-step 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 \\ (0.3A)/(0.3)=(0.2B)/(0.3) \\ A=(2)/(3)B \end{gathered}`

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

`\begin{gathered} A+B=120 \\ (2)/(3)B+B=120 \\ (5)/(3)B=120 \\ 3\cdot(5)/(3)B=3\cdot120 \\ 5B=360 \\ (5B)/(5)=(360)/(5) \\ B=72 \end{gathered}`

Finally, A is equal to:

`\begin{gathered} A=(2)/(3)B \\ A=(2)/(3)(72) \\ A=48 \end{gathered}`

Therefore, she should use 48o

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