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a scientist has two solution, which she labeled solution A and solution B. each contains salt. she knowns that solution A is 60 % salt and solution B is 85% salt. she want to obtain 110 ounces of a mixture that is 75% salt. how many ounces of each solution should she use

Respuesta :

The scientist has to take x ounces of the solution A and B of the solution B, so that

[tex]x+y=110[/tex]

The amount of salt S this solution has is

[tex]S=0.6x+0.85y[/tex]

Since we need a solution with 75% salt, then we need that

[tex]\begin{gathered} \frac{S}{110}=0.75 \\ \frac{0.6x+0.85y}{110}=0.75 \\ 0.6x+0.85y=82.5 \end{gathered}[/tex]

Then, we have the system of linear equations

[tex]\begin{gathered} x+y=110 \\ 0.6x+0.85y=82.5 \end{gathered}[/tex]

Solving for x in the first equation and replacing in the second

[tex]\begin{gathered} x=110-y \\ 0.6(110-y)+0.85y=82.5 \\ 66-0.6y+0.85y=82.5 \\ 0.25y=16.5 \\ y=66 \\ x=110-66=44 \end{gathered}[/tex]

Then, if we take 44 oz of A and 66 of B we have

[tex]0.6(44)+.85(66)=82.5[/tex]

In conclusion, the scientist needs to take 44 oz of the solution A and 66 oz of solution B.

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