Would you please help me with this math problem?

I’m not sure where you got “4 parts of 100% plus 95 parts of 1%,” but that adds up to only .04 + .95 = 99%.

Let’s say you add x grams of yellow mercuric oxide (ymo).
I’m assuming percentages are by mass, so volume is irrelevant.

The final total mass of the mixture is 30 + x (because you added x)
The initial mass of ymo was (30g)(1%) = 0.3 grams
The final mass of ymo is therefore x + 0.3 (because you added x) ***

The final concentration is 5%, so final mass of ymo is (30+x)(5%)
= (30 + x)(.05)
= 1.5 + .05x ***

Equating the two starred equations above *** for mass of ymo:
x + 0.3 = 1.5 + .05x
.95x = 1.2
x = 1.2/.95 = 1.263… grams of ymo added.

So the final ointment contains 1.563… g of ymo in a total mass of 31.263… grams, which is exactly 5%.

Perfect @gasman. I completely understand where you got that 1.26g answer, because you explained it so well. I’ll learn that and apply it to the next problem I have and I’d give you 1000 GAs for your answer.

However it doesn’t fit my textbook and I can’t reconcile it with the methods we are supposed to be learning (and what I am supposed to be tutoring to my fellow students).

We are being taught alligation. To end up with 5%, you have the 5 in the middle of a box; the 100 at the top left and the 1 at the bottom left. That means you have 99 total parts; 4 parts are of the 100% and 95 parts are of the 1%. It doesn’t have to add up to 100: most times the alligation adds up to much less than 100, but from there you can figure amounts IF you have a final volume.

@Blueroses The truth is I never heard of alligation until you mentioned it. I just like to work algebra problems, I guess, but you should learn the methods they teach you. Good luck!

@gasman The alligation for my field looks like this

From there, I would set up a ratio/proportion or a dimensional analysis and solve, but I can’t use either of those methods without a total volume. Your algebra method works for me, and again I thank you for that, but is there any way to derive that answer using one of the methods we are being taught? If there is not, then it is a bad question and should be discarded from the test.

After letting this problem simmer for 24 hours, the very simple solution came to me out of the blue. Thank you @gasman for explaining an alternate method. It put my brain on the right track.

If anybody’s interested, this is the simple proportion I came up with:

Xg (100%)/4 parts = 30g (1%)/95 parts
Cross multiply to get 95x = 120
Divide both sides by 95
X=1.26