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Question 242296: A chef is using a mixture of two brands of Italian dressing. The first brand contains 8% vinegar, and the second brand contains 13% vinegar. The chef wants to make 320 milliliters of a dressing that is 11% vinegar. How much of each brand should she use?
Answer by kelli_scofield(5)   (Show Source):
You can put this solution on YOUR website! I am a visual learner, so I try to draw a picture to help me understand a word problem. In a mixture problem, you are working with an amount(ml) and a concentration(%).
I draw 3 lines ___+___=___ (I usually use boxes instead of lines to combine the #'s and variables)
Let your first brand = x
Let your second brand = y
You do not need a variable for the product because you have an amount and a concentration already. Use the variables (x and y) to replace your unknowns. The unknowns are the amounts of the first and second brands.
x+y=320 (this is your equation for the amounts)
0.08x +0.13y=.11(320) (this is your equation for the concentrations)
We can use the substitution or elimination method to solve this. I will use the substitution method. I don't like using decimals, so I am going to move the decimal place two units to the right to make them whole numbers. This gives me: 8x+13y=11(320)
Using substitution on the first equation, I put X on one side of the equation. This gives me x=(-y+320). I can now substitute (-y+320) for x in the second equation.
8(-y+320)+13y=3520
-8y+2560+13y=3520
Subtract 2560 from both sides and combine 13y and -8y. This gives you 5y=960. Divide both sides of the equation by 5. This gives you y=192.
y=192
x=128
I got x by plugging y into equation #1.
x+(192)=320. After subtracting 192 from 320, I get x= 128.
To check your answer, always substitute x and y in for both equations.
ANSWER: The chef should use 128 milliliters of the 8% vinegar brand and 192 milliliters of the 13% vinegar brand.
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