Answer:
The chef needs 50 milliliters of the first brand
The chef needs 150 milliliters of the second brand
Explanation:
A chef is going to use a mixture of two brands of Italian dressing.
Let x = the amount (in milliliter) of the first brand of Italian dressing .
Let y = the amount (in milliliter) of the second brand of Italian dressing .
The first brand contains 9 % vinegar
This means that it contains 9/100 × x
= 0.09x
The second brand contains 13 % vinegar
This means that it contains 13/100 × y
= 0.13y
The chef wants to make 200 milliliters of a dressing that is 12 % vinegar. This means that the amount of vinegar in the mixture would be
12/100 × 200 = 24
Also, the volume of first + the volume of second brand will be 200 milliliters ( volume of mixture). This means
x + y = 200 - - - - - - - -1
The combined amount of vinegar in both brands = the amount of vinegar required in the mixture. This means
0.09x + 0.13y = 24 - - - - - - - - 2
Substituting x = 200 - y into equation 2, we have
0.09(200-y) + 0.13y = 24
18 - 0.09y + 0.13y = 24
-0.09y +0.13y = 24-18
0.04y = 6
y = 6/0.04 = 150 milliliters
x = 200 - y = 200 - 150
x = 50 milliliters