Answer :
The chef should mix 14.67 ounces of pure vinegar with 113.33 ounces of mild dressing to make 128 ounces of a 15% vinegar-to-oil salad dressing.
What is the linear equation?
The formula for simple linear regression is Y = mX + b, where Y is the response (dependent) variable, X is the predictor (independent) variable, m is the estimated slope, and b is the estimated intercept.
Let's call the number of ounces of pure vinegar the chef should use "x" and the number of ounces of the mild dressing he should use "y".
We know that the chef wants to end up with 128 ounces of dressing, so we can write:
x + y = 128
We also know that the resulting mixture should be 15% vinegar, which means that the amount of pure vinegar in the mixture will be 0.15 times the total volume of the mixture. Similarly, the amount of vinegar in the mild dressing will be 0.04 times the total volume of the dressing or 0.04y.
So the total amount of vinegar in the final mixture will be:
0.15(128) = 19.2 ounces
And we can set up another equation based on this:
x + 0.04y = 19.2
Now we have two equations with two variables:
x + y = 128
x + 0.04y = 19.2
We can solve this system of equations using substitution or elimination. Here's how to do it using substitution:
x + y = 128 (Equation 1)
x + 0.04y = 19.2 (Equation 2)
Solve Equation 1 for x:
x = 128 - y
Substitute this expression for x in Equation 2:
(128 - y) + 0.04y = 19.2
Simplify and solve for y:
128 - 0.96y = 19.2
-0.96y = -108.8
y = 113.33
So the chef should use 113.33 ounces of the mild dressing and:
x = 128 - y = 128 - 113.33 = 14.67
ounces of pure vinegar.
Therefore, the chef should mix 14.67 ounces of pure vinegar with 113.33 ounces of mild dressing to make 128 ounces of a 15% vinegar-to-oil salad dressing.
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Complete question:
A chef wants to make 1 gallon (128 ounces) of a 15% vinegar-to-oil salad dressing. He only has pure vinegar and a mild 4% vinegar-to-oil salad dressing on hand. How many ounces of each should he mix to make the desired dressing
Final answer:
Given the incomplete question, an approximate answer would be that if a chef adds a certain amount of vinegar to each batch of salad dressing, half of a batch would require half of that amount. This is because the quantity of vinegar used is proportional to the batch size.
Explanation:
It looks like the question is incomplete. Regardless, based on the information available, if a chef adds a certain amount of vinegar (in gallons) to each batch of salad dressing, the amount of vinegar used in half of a batch would likely be half of that amount. For instance, if they normally add 2 gallons of vinegar per batch, half of a batch would require 1 gallon of vinegar.
That's because the amount of vinegar is proportional to the size of the batch. If the batch size is halved, the amount of vinegar should also be halved.
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