where are the solutions to these homework questions i am having a difficult time solving these Avg/media/mode problems from the lessons
I think that is an ETS question, so you might find it somewhere. Also, I think you cand find all of the answers in the session right after the one where you found such problem, so just check out the videos. If you still find yourself having some trouble with the problem, you can post your question on the forum and there’s people who can give you a different perspective.
So if you want to know the answer to this particular question, consider that solution R has 8% of liquid A and that solution S has 18% of liquid A. Notice that the question is asking about what the concentration of liquid A will be of the resulting mixture. I like thinking of the problem in this way. So if I have 3 grams of solution R, that means that I have \frac{8}{100} \cdot 3 of liquid A in those 3 grams, because we know that no matter what the amount of solution R, there will always be 8% of liquid A. Similarly, in 7 grams of solution we have \frac{18}{100}\cdot 7 of liquid A for the reason we just mentioned. Since I am combining both numbers, it makes sense to add them up, right? So, our resulting solution will be \frac{8}{100}\cdot 3 + \frac{18}{100}\cdot 7. Now, we know that this will result in a particular percent concentration of liquid A, which is what the question is asking. Thus, we have our equation at hand: \frac{8}{100}\cdot 3 + \frac{18}{100}\cdot 7 = \frac{x}{100} (3+7). Why do we have 3+7 on the right hand side? Because we are combining 3 grams of R and 7 grams of S, so when we mix them up, we would have 10 grams total. Hope this helps you with some intuition.