A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 16% vinegar. The chef wants to make 210 milliliters of a mixture that contains 48% vinegar. How much vinegar and how much Italian dressing should she use?

now, how much vinegar is in the dressing anyway?  now, the dressing contains other substances, but just vinegar, we know is 16% in it, therefore, if we use say "y" mL of dressing, how much is 16% of y?  well, (16/100) * y, or 0.16y.  So that much vinegar will be in that "y" mLs.

now, we're also mixing pure vinegar, how much vinegar is in pure vinegar?

well, is pure vinegar, so is 100% vinegar, so if we use say "x" mL, that'll be (100/100) * x, or 1.00x or just x.

and the mixture we know needs to be 210mLs at 48% vinegar, so that'd be (48/100) * 210 or 100.8 of vinegar in the mixture.

bear in mind that whatever "x" and "y" are, they must yield 210 for the mixture, thus x + y = 210.

and the vinegar quantities, must also yield the mixture requirement, thus x + 0.16y = 100.8.

[tex]\bf \begin{array}{lccclll} &\stackrel{mL}{amount}&\stackrel{vinegar~\%}{quantity}&\stackrel{vinegar~mL}{quantity}\\ &------&------&------\\ \textit{pure vinegar}&x&1.00&1.00x\\ \textit{16\% vinegar dressing}&y&0.16&0.16y\\ ---------&------&------&------\\ mixture&210&0.48&100.8 \end{array}[/tex]

[tex]\bf \begin{cases} x+y=210\implies \boxed{y}=210-x\\ x+0.16y=100.8\\ ----------\\ x+0.16\left( \boxed{210-x} \right)=100.8 \end{cases} \\\\\\ x-0.16x+33.6=100.8\implies 0.84x=67.2 \\\\\\ x=\cfrac{67.2}{0.84}\implies x=\stackrel{mL}{80}[/tex]

how much will it be of the dressing?  well, y = 210 - x.