Math people, please help me understand this

Thinking about it, I should have known that. It's the same thing we talked about in my Math in Video Games thread in Gaming, just not as complicated. I'm sure you remember (@Patman, especially) that in Arc the Lad: Twilight of the Spirits that, with the exception of Medical Machine because it completely restores health, healing abilities restore a fixed percentage of your health based on your current maximum health.

For example, Cure heals 25% of a target's maximum health. If maximum health equals 237, then to find the answer, we would do the following:

x over 237 times 25% over 100%. 237 times 25 divided by 100 would give us our answer of 59 (59.25). The source, as you put it, in this case would be 237?

However, the source is not always clear. In the case of my problem above, though, it's more or less clear that six should go over 75 and x should go over 325.

 

Yeah I was struggling for a way to phrase that and it didn't really come out right. Basically some values get linked together. In your pushup example you know two pieces of information at any moment; how long you've been doing pushups and how many pushups you've done. The two aren't independent from each other so you need to keep in mind which moment was your "source" for that piece of information.

So at moment "a" we have
Time at a = 6 minutes
Pushups at a = 75

And at moment "b" we have
Time at b = x
Pushups at b = 325

But you can't take time at a and relate it to pushups at b since they don't have anything to do with each other. They are describing two different moments. Sorry if my choice of terms is confusing at all.

 

That explains it better, thanks.

Perhaps you or someone else can help me with the problems I couldn't get: After trying them repeatedly, when I kept everything properly linked, I got 8/13 and 16 as answers, but the book is saying the answers are 41.6, which maybe 8/13 converts to, and four.

x/16 = 10/26 (26x = 16 * 10) = 8/13

x/20 = 40/50 (50x = 20 * 40) = 16

Both are essentially the same type of word problem, so if I can at least figure out one, then... Of course I'm going to ask my instructor, too, but if I can get a general idea, it'll probably help in the long run.

 

I think I learned to solve those things differently, I recognize neither your method nor your lingo.
We call those "produits en croix" (cross multiplications).
In the case of the first shadows problem it would look like this :



You just multiply the two numbers pointed by each line of the red cross, one multiplication equals the other.
So in this case 10x = 26*16
x= (26*16)/10

 

This thread is making me grateful I'm taking a statistics class this semester because the farthest I've had to go so far is sample standard deviation.

Then again if you make one small mistake with simple math you're ****ed.

 

Second problem would look like this :

Spoiler

50x = 20*10
x = 200/50 = 4

 

The first one is easy, since you just cross multiply
10/26 = 16/X

10x = 416

X = 41.6


The second I was getting wrong too, but that's because I forgot the subtraction of 50 and 40 in the example Patman just showed. Try to always get the numbers together before just grouping them in the order they appear. You have a 20 foot tree that casts a 50 foots shadow, so you have 20/50 for your first number. Your trying to get X, which is your size, so you have X on the top, and then you have 50, which is the length of the shadow, minus 40, being the length you are from the tree, giving 10, being your shadow length...or something along those lines. It makes sense in my head, but I can't say the same if it makes sense for you.

 

Obviously, I'm doing something wrong. I have the numbers in the same place as you do for the first one. I'll have to work it out again after Spanish 101 during my break.

As for the second one, there's no multiplication involved, then?

 

Sorry, I'm not very good at explaining math, especially if I can't write it down. But you have multiplication, you just need to get your numbers first. So you have the size of the tree, 20ft, and the length of it's shadow, 50ft, this gives you the number 20/50.

The second number you need the size of your height, so Xft, and you need the size of your shadow, so you take the length of the tree's shadow, minutes how far you are from the tree, since the question states that you will still be in the shadow, so 50-40, giving you 10 feet is your own shadow, so you have X/10.

Now with those numbers, you have the equation 20/50 = x/10

now with cross multiplication you get 50x = 200

dividing 50 from both sides you get x = 4

so 4ft is how tall you must be standing 40ft from the tree with a 50ft shadow to be completely in the shadow

 

So I just wasn't plugging the numbers in correctly. After looking at the questions closer, I realized why @Patman's orders were correct. Although it's confusing at first.

 

Patman's is the same a lot of people do, he just had the extra boxes around with the words, which no one ever does on paper. All you have to do is make sure you get your numbers in the right spot and do the cross-multiplication right.

 

I was getting the units matched correctly for the most part (e.g., hours / miles = hours / miles is correct while hours / miles = miles / hours is incorrect), but I wasn't matching them to the source, as @Mixt mentioned.

 

Well that' s just it, if he' s having trouble getting his numbers at the right place then writing the words down will help him to avoid brain farts.

 

Just depends on the person. When I had to do those questions in High school I just linked them together and would write in air getting the stuff in my head right. It's more of a matching game than anything else

 

Getting the link can be the problem, though. Going back to my earlier example:

I had 75/x = 325/6, which was incorrect. While both fractions matched (pushups / minutes = pushups / minutes), I had the numbers in the wrong places. It should have been 75/6 = 325/x.

 

but looking at it, what relates to what? It says in the beginning that within 6 minutes the enthusiast can do 75 pushups. Those relate to each other. It's asking how long it would take to do 325 pushups only, meaning there was no time to relate to the larger amount of pushups like it did with the first amount, being 6 minutes, so you had to find that unknown.

 

You just made Geometry cry

 

You just made Geometry cry.

 

I realized that not 2 seconds ago. Haha

I can't seem to get Geology, Geometry, and Geography straight in my head