The chef will end up with 300 mL of a dressing that is 9% vinegar. Let's calculate how much vinegar will the dressing have:
Therefore,
[tex]v=\frac{300\times9}{100}\rightarrow27[/tex]He'll have 27mL of vinegar.
Now, we know that x mL of the 5% dressing plus y mL of the 15% one will give the chef a total of 27mL of vinegar. Therefore,
[tex]\begin{gathered} x(\frac{5}{100})+y(\frac{15}{100})27 \\ \\ \rightarrow0.05x+0.15y=27 \end{gathered}[/tex]And that x mL of the 5% dressing plus y mL of the 15% one will give the chef a total of 300mL of dressing. Therefore,
[tex]x+y=300[/tex]We have a system of equations:
[tex]\mleft\{\begin{aligned}0.05x+0.15y=27 \\ x+y=300\end{aligned}\mright.[/tex]Let's clear y from equation 2 and replace in equation 1:
[tex]\begin{gathered} x+y=300\rightarrow y=300-x \\ \\ 0.05x+0.15y=27\rightarrow0.05x+0.15(300-x)=27 \\ \rightarrow0.05x+45-0.15x=27\rightarrow-0.10x=-18\rightarrow x=\frac{-18}{-0.10} \\ \\ \rightarrow x=180 \end{gathered}[/tex]Thereby,
[tex]\begin{gathered} y=300-x\rightarrow y=300-180 \\ \\ \rightarrow y=120 \end{gathered}[/tex]The chef would have to use 180mL of the dressing that's 5% vinegar, and 120mL of the one that's 15% vinegar.
