Help with Algebra II word problems! How to set it up and solve it algebreically.?

Question

Here's the problem, word for word:
Distilled white vinegar purchased in supermarkets generally has a 5% acidity level. Chef Judy marinates her veal in a special 8% vinegar that she creates herself. To create the 8% solution she mixes the 5% with a special 12% she purchases by mail. How many ounces of the 12% vinegar does she need to add to 40ounces of the 5% vinegar to get the 8% vinegar?

Answer 1

X = Ounces of 12% vinegar needed
X(0.12)+40(0.05)=(40+X)0.08
12X+200=320+8X
4X=120
X=30

Answer 2

So we've got vinegar being mixed together, and each jar of vinegar contains a certain amount of acid, which is expressed as a percentage of the vinegar.

Now, the key to mixture problems is to organize your information well (some people draw charts, others draw pictures -- neither of which can be easily done on Yahoo Answers, unfortunately). You also have to be clear on three simple but crucial concepts:

[1.] In each jar of vinegar, you can get the actual volume of acid by multiplying the volume of vinegar by the acid percentage.
[2.] The total volume of vinegar in the mix is the sum of the vinegars in the two contributing jars -- no vinegar "magically" appears or disappears when you mix the two jars together.
[3.] The same is true for the volume of acid, which is maybe a little less obvious but just as true.

So, first of all, let's summarize our info. The thing we're supposed to find is the amount of 12% vinegar, in ounces. We'll use x to represent that.

Jar 1 has 40 ounces of the 5% vinegar.
Jar 2 has x ounces of the 12% vinegar.
Jar 3 *must have* (x + 40) ounces of the resulting 8% vinegar mix. [See point 2 above.]

Now, from [point 1], we can determine how much acid is in Jar 1: (40 oz)(5%) = (40 oz)(0.05) = 2 oz. of acid.
We can do the same for the other two jars, although the results will be math expressions, not simple numbers. Jar 2 must have (x oz)(12%) = 0.12x oz. of acid, and Jar 3 must have (x+40)(8%) = 0.08(x + 40) oz. of acid.

Finally, from [point 3] above, the acid must add up. The 2 oz. from Jar 1, combined with the 0.12x oz. from Jar 2, must equal the 0.08(x + 40) oz. in the mixture in Jar 3, and that's our equation:

2 + 0.12x = 0.08(x + 40)

Now you just have to solve this for x. And, by the way, if you dislike decimals, you can multiply both sides by 100 to get rid of them all, *but* I strongly recommend distributing the 0.08 over the x + 40 first... you'll be less likely to make mistakes that way.

Good luck!

Answer 3

if x is the number of ounces of supermarket vinegar and y is the number of ounces of special vinegar then we can set up the problem this way:

.05x + .12y = .08(x+y)

You have x, solve for y

Answer 4

We assume % here is by weight.
40 oz of vinegar has(5%)or 2 oz acid
let x oz of vinegar(12%) be added. it has .12x acid
therefore
40+x vinegar must have 2+.12x oz acid which is 8%
(40+x)*.08=2+.12x
3.2+.08x=2+.12x
.04x=1.2
x=30oz
verify--
40oz acid content=2oz(5%)
30 ozacid content=3.6(12%)
total acid content=5.6 oz
70 oz acid content=5.6(8%)
verified

Answer 5

x*0.12+40*0.05=(40+x)0.08
12x+200=320+8x
4x=120
x=30
she has to add 30 Oz

Answer 6

.05 (40) + .12x = .08 (40 + x)

You can solve it.