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?
Accepted Solution
A:
Answer: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/mL8%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/mL8% .0813% .13total % 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/mL8% .0813% .13total % 380 .12If 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/mL8% x * .08 = .08x13% 380 - x * .13 = .13(380 - x)total % 380 * .12 = 45.6Since 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 and8x + 4940 - 13x = 4560 and-5x = -380 sox = 76This means that there is 76 mL of 8% and 380 - 76 = 304 mL of 13%