Question

A chef plans to mix 100% vinegar with italian dressing. the italian dressing contains 7% vinegar. the chef wants to make 310 milliliters of a mixture that contains 19% vinegar. how much vinegar and how much italian dreessing should she use ?

vinegar: ? milliliters
italian dressing: ? milliliters

Answer 1

Let
`x` be the amount (mL) of the pure vinegar the chef will use, and
`y` the amount of dressing. She wants to end up with a 310 mL mixture, so

`x+y=310`

For each mL used of the dressing, 0.07 mL is vinegar, and the chef wants to end up with a 19% vinegar mixture, so

`x+0.07y=0.19(x+y)=58.9`

Now

`x+y=310\implies y=310-x`

`\implies x+0.07(310-x)=58.9`

`\implies0.93x+21.7=58.9`

`\implies0.93x=37.2`

`\implies x=40`

`\implies y=270`