Question about ratios, proportions and percents

[AznBoi]

Does it matter what order you put ratios and proportions in? For example:
The weight of the tea in a box of 100 identical tea bags is 8 ounces. What is the weight, in ounces, of the tea in 3 tea bags?

Here is the provided solution to the problem:
x/8=3/100

100x=24

x=.24


Here is my solution to the problem:
100/8=3/x (100 tea bags is 8 ounces)=(3 tea bags is x ounces)

100x=24

x=.24
I mean, why would they give the solution they provided?? Doesn't my solution prove to be easier. If 100 is 8 ounces, then 3 bags is x ounces.

Which method is correctly used? Does my method work for any type of proportion problem? It seems to me that both of these are the same, just differently set up and thought about.

Does it matter what order you put your ratio in? as long as the order is consistent throughout the problem? I just want to get this straight because a lot of my answers do not match up with solutions but have the same answer. Which method should I use? What method would you use?

If you don't mind and have time, please answer most, if not all of my questions. However, even the smallest insight would be appreciated! I'm very anxious to hear about these kind of problems. This will definitely help me out in the future, especially for the SAT.

 

[arildno]

While your method is as good as the book's, I would favour the following approach:

The folllowing statement HAS to be true:
The weight for ONE teabag remains the same for both situations! (*)

Now, the weight for ONE teabag is in the first example evidently 8/100, whereas the weight ONE teabag in the other example is x/3.

Thus, according to (*), we have the equation:
x/3=8/100, which of course yields x=0.24

Note that the book's rationale is that "the weight ratio must equal the number of teabags ratio", whereas YOUR equation states "the number tea bags per unit weight must be equal in both cases"

Which of these three statements do you find simplest to understand?

 

[AznBoi]

How is it the weight of ONE teabag? I don't really get what the question is asking either.

The weight of the TEA in a box of 100 identical tea bags.. So I guess you were right, they are referring to the weight of the TEA BAG?

At first I thought that they said the weight of 100 tea bags is 8, and 3 tea bags is x. I guess that is wrong huh?

"What is the weight, in ounces, of the tea in 3 tea bags?" What is that asking, at first it asked for the weight of the TEA in a box..

Ugh, can someone explain this to me..

 

[cristo]

The question is asking for the weight of three tea bags.

You can think of the solution in an equivalent way, as finding the weight of one tea bag, then multiplying this by 3.

i.e. x=(8/100)*3.

 

[AznBoi]

ohhh.. I see. thanks!

 

[HallsofIvy]

Order does matter slightly: you have to be consistent. A "ratio" is a fraction and a "proportion" is an equation saying that two fractions are equal. You have to set the fractions up so that the units are the same. For example, your book is setting the two fractions to be x ounces/8 ounces and 3 teabags/100 teabags. Since the numerator and denominator of each fraction have the same units the fractions themselves are "dimensionless". You, on the other hand, are using the fractions 100 teabags/ 8 oz and 3 teabags/x ounces. Now the fractions are not dimensionless but they do have the same units: teabags/oz.

I'm not sure I would agree that your method is "easier". Certainly for you, it is- because you think "If 100 is 8 ounces, then 3 bags is x ounces. " Some people might prefer to think "100 tea bags is to 3 as 8 ounces is to x". May people might even prefer to set it up as "8 ounces/100 teabags= x ounces/3 teabags" which is what Cristo is doing.