SOLUTION: A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand contains 13% vinegar. The chef wants to make

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand contains 13% vinegar. The chef wants to make       Log On


   

Question 1104637: A chef is going to use a mixture of two brands of Italian dressing. The first brand contains
7%
vinegar, and the second brand contains
13%
vinegar. The chef wants to make
300
milliliters of a dressing that is
12%
vinegar. How much of each brand should she use?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
x, volume of the 7% vinegar
300-x, volume of the 13% vinegar

7x%2B13%28300-x%29=12%2A300
-
7x%2B13%2A300-13x=12%2A300
-6x=12%2A300-13%2A300
6x=1%2A300
x=300%2F6
highlight%28x=50%29
-
300-x=highlight%28250%29

Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


I find the method of alligation is much faster than the traditional algebraic method (shown by the other tutor) for solving most mixture problems that involve mixing just two ingredients.

Here is my version of the method of alligation used to solve this particular problem.

Think of the three percentages on a number line: 7, 12, and 13.
The 12 is 5/6 of the way from 7 to 13. (12-7=5; 13-7=6)
That means 5/6 of the mixture must be the dressing containing 13% vinegar.
5/6 of 300 is 250; so he needs to use 250ml of the dressing with 13% vinegar and 50ml of the dressing with 7% vinegar.

Here is a diagram that can provide an alternative method for solving the problem using the method of alligation:

matrix%283%2C3%2C13%2C%22%22%2C5%2C%22%22%2C12%2C%22%22%2C7%2C%22%22%2C1%29

The 13 and 7 in the first column are the percentages of vinegar in the two ingredients; the 12 in the middle column is the desired percentage of vinegar.
The numbers in the third column are the differences, computed diagonally, between the numbers in the first and second columns: 13-12=1; 12-7=5.
Those numbers in the third column tell the ratio in which the two ingredients must be mixed: 5 parts of the 13% ingredient to 1 part of the 7% ingredient.