A chef is going to use 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 380 milliliters of a dressing that is 12% vinegar. How much of each brand should she use?

76 mL of 8% and 304 mL of 13%

Step-by-step explanation:

Set up a table like this (this is the same table for any mixture problem):

mL total * % vinegar = % vinegar/mL

8%

13%

total %

What you do with this table is multiply the first 2 columns and they equal the last column. We already know the middle column's entries from what we are given. But remember that a percent needs to be expressed as a decimal:

mL total * % vinegar = % vinegar/mL

8%.08

13%.13

total %

Now we also know that the total he wants to make is 380 mL that is 12%, so all that info goes into the last row:

mL total * % vinegar = % vinegar/mL

8%.08

13%.13

total % 380.12

If he wants this total mixture to come from the 8% and the 13% vinegars, he is mixing them together, or adding them. We need to know how much 8% + how much 13% will give us 380 mL of 12%. So we can fill in the amounts accordingly. If he has x mL of 8%, then he will have 380 - x of 13%. The table tells us that we are multiplying the first 2 columns to get the third, so we will do that at the same time:

mL total * % vinegar = % vinegar/mL

8% x *.08 =.08x

13% 380 - x *.13 =.13 (380 - x)

total % 380 *.12 = 45.6

Since we are adding the different vinegars together to get the total, we can do that with the last column as well. This is our equation:

.08x +.13 (380 - x) = 45.6 Multiply everything through by 100 to get rid of the decimals now:

8x + 13 (380 - x) = 4560 and

8x + 4940 - 13x = 4560 and

-5x = - 380 so

x = 76

This means that there is 76 mL of 8% and 380 - 76 = 304 mL of 13%