A chef is using a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand contains 11% vinegar. The chef wants to make 280 milliliters of a dressing that is 10% vinegar. How much of each brand should she use?
first brand?
second brand?
solve
.07x + .11(280-x) = .1(280)
174
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the chef uses x milliliters of the first brand and y milliliters of the second brand.
The first equation represents the total volume of the dressing:
x + y = 280 --> Equation 1
The second equation represents the percentage of vinegar in the mixture:
(0.07x + 0.11y)/(x + y) = 0.10 --> Equation 2
To solve the system of equations, we can use a method called substitution.
From Equation 1, we can rewrite it as:
x = 280 - y
Substitute this value of x into Equation 2:
(0.07(280 - y) + 0.11y)/(280) = 0.10
Now, let's solve for y:
(0.07(280 - y) + 0.11y)/(280) = 0.10
(19.6 - 0.07y + 0.11y)/(280) = 0.10
(19.6 + 0.04y)/(280) = 0.10
1960 + 4y = 2800
4y = 840
y = 210
Now, substitute y = 210 back into Equation 1 to find x:
x = 280 - y
x = 280 - 210
x = 70
Therefore, the chef should use 70 milliliters of the first brand and 210 milliliters of the second brand to make a dressing that is 10% vinegar.