Question

A chef is going to use a mixture of two brands of Italian dressing. Thefirst brand contains 1% vinegar, and the second brand contains 12%vinegar. The chef wants to make 230 milliliters of a dressing that is 11%vinegar. How much of each brand should she use?

Answer 1

20.91 milliliters of the 1% vinegar and 209.09 milliliters of the 12% vinegar

Step-by-step explanation:

let the amount used from the 1% vinegar = x

let rhe amount used from the 12% vinegar = y

the concentration of the mixture = 11%

The chef wants to make 230 milliliters of a dressing

This means the sum of the amounts sed in both concentration gives = 230 milliliters

x + y = 230 ...(1)

The concentration for each vinegar:

1%(x) + 12%(y) = 11% (230)

0.01(x) + 0.12y = 0.11(230)

0.01x + 0.12y = 25.3 ....(2)

Using substitution method:

from equation (1), we can make x the subject of formula:

x = 230 - y

substitute for x in equation (1):

0.01(230 - y) + 0.12y = 25.3

0.01(230) - 0.01(y) + 0.12y = 25.3

2.3 - 0.01y + 0.12y = 25.3

2.3 + 0.11y = 25.3

0.11y = 25.3 - 2.3

0.11y = 23

y = 23/0.11

y = 209.09

substitute for y in equation 1:

x + 209.09 = 230

x = 230 - 209.09

x = 20.91

Hence, the chef will use 20.91 milliliters of the 1% vinegar and 209.09 milliliters of the 12% vinegar