Answer:
76 mL of 8% and 304 mL of 13%
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%