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Sagot :
Since she wants to obtain 150 ounces of the mixture of A and B, then
Add A and B, then equate the sum by 150
[tex]A+B=150\rightarrow(1)[/tex]Since 40% of A is salt
Since 65% of B is salt
Since 150 ounces has 55% salt, then
[tex]\begin{gathered} \frac{40}{100}A+\frac{65}{100}B=\frac{55}{100}(150) \\ \\ 0.40A+0.65B=82.5\rightarrow(2) \end{gathered}[/tex]Now, we have a system of equations to solve it
Multiply equation (1) by -0.40 to make the coefficients of A equal in values and opposite in signs
[tex]-0.40A-0.40B=60\rightarrow(3)[/tex]Add equations (2) and (3)
[tex]\begin{gathered} (0.40A-0.40A)+(0.65B-0.40B)=(82.5-60) \\ \\ 0+0.25B=22.5 \\ \\ 0.25B=22.5 \end{gathered}[/tex]Divide both sides by 0.25
[tex]\begin{gathered} \frac{0.25B}{0.25}=\frac{22.5}{0.25} \\ \\ B=90 \end{gathered}[/tex]Substitute B in equation (1) by 90 to find A
[tex]A+90=150[/tex]Subtract 90 from each side
[tex]\begin{gathered} A+90-90=150-90 \\ \\ A=60 \end{gathered}[/tex]There are 60 ounces of A and 90 ounces of B
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