Question

A chef plans to mix 100% vinegar with Italian dressing. The Italian dressing contains 12% vinegar. The chef wants to make 320 milliliters of a mixture that contains 23%vinegar. How much vinegar and how much Italian dressing should she use?

Answer 1

Answer:

40 mL of vinegar,

280 mL of dressing

Step-by-step explanation:

Let v = the milliliters ( mL ) of 100% vinegar,

Then it should be that 320 - v = mL of dressing.

v + .12( 320 - v ) = .23( 320 ) - So in this case the mL of vinegar is associated with the percent of vinegar composed. 100 percent is, in other words, 1, and is multiplied by " v " the mL of 100% vinegar. 1 $*$ v is also v, and so is written as such in our equation. 0.12 is the decimal form of the 12% vinegar, associated with the mL of dressing - as the italian dressing is composed of 12% vinegar. 23% is 0.23 in decimal form, multiplied by the mL of of vinegar in the mixture, 320 mL.

Let's solve for the mL of 100% vinegar, subtracting from 320 to receive the mL of dressing,

v + .12( 320 - v ) = .23( 320 ) - Distribute " .12 "

v + 38.4 - 0.12v = .23( 320 ) - Multiply " 0.32 " by " 320 "

v + 38.4 - 0.12v = 73.6 - Combine like terms and add / subtract

0.88v = 35.2 - Divide 0.88 on either side

v = 40 mL of vinegar,

320 - v = 320 - 40 = 280 mL of dressing