SOLUTION: A chef is using a mixture of two brands of Italian dressing. The first brand contains 5% vinegar and the second brand contains 10% vinegar. The chef wants to make 200mL of a dressi

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Question 998476: A chef is using a mixture of two brands of Italian dressing. The first brand contains 5% vinegar and the second brand contains 10% vinegar. The chef wants to make 200mL of a dressing that is 8% vinegar. How much of each brand should the chef use?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Some variables,
system%28L=5%2CH=10%2CT=8%2CM=200%2Cu=volumeLowConc%2Cv=volumeHiConc%29

EQUATIONS FROM WHICH TO SOLVE FOR u AND v
system%28%28Lu%2BHv%29%2FM=T%2Cu%2Bv=M%29

Converting the system into a single equation with only one variable can be done near the beginning, as in this example video:
two-part mixture using just one variable

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A chef is using a mixture of two brands of Italian dressing. The first brand contains 5% vinegar and the second brand contains 10% vinegar. The chef wants to make 200mL of a dressing that is 8% vinegar. How much of each brand should the chef use?
Let amount of 5% vinegar to mix, be F

Then amount of 10% vinegar to mix = 200 - F

We then get: .05F + .1(200 - F) = .08(200)

.05F + 20 - .1F = 16

.05F - .1F = 16 - 20

- .05F = - 4

F, or amount of 5% vinegar to mix = %28-+4%29%2F%28-+.05%29, or highlight_green%2880%29 mL

You should be able to find amount of 10% vinegar that needs to be mixed