Question about ratios, proportions and percents

  • Thread starter AznBoi
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It's a matter of preference. What is important is that you set it up correctly. If you do so, and follow through correctly, you will get the correct answer. Personally, I prefer Cristo's method because it is the most general. Suppose we had 100 tea bags which weigh 12 ounces. How much do 3 tea bags weigh? Using your method, you would have to redo everything. Using Cristo's method, you would simply change the numbers and continue. In particular, suppose we had 100 tea bags which weigh 12 ounces. How much do 4 tea bags weigh? With your method you would have to start completely over. With Cristo
  • #1
AznBoi
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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. :smile:
 
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  • #2
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?
 
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  • #3
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.. :frown:
 
  • #4
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.
 
  • #5
ohhh.. I see. thanks!
 
  • #6
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.
 

What is the difference between a ratio, a proportion, and a percent?

A ratio is a comparison between two quantities, usually expressed in the form of a fraction. A proportion is an equation that states that two ratios are equal. A percent is a ratio that compares a number to 100.

How do you solve problems involving ratios?

To solve a ratio problem, you can use the following steps:
1. Write the given ratio in the form of a fraction.
2. Find the common factor between the two numbers in the ratio.
3. Simplify the fraction to its lowest terms.
4. Multiply or divide both numbers in the ratio by the same factor until you reach the desired result.

How can ratios be used in real-life situations?

Ratios are used in many real-life situations, such as cooking (where ingredients are often measured in ratios), financial planning (where ratios can be used to compare expenses and income), and sports (where ratios can be used to track statistics).

What is the relationship between ratios and proportions?

The relationship between ratios and proportions is that a proportion is a statement that two ratios are equal. In other words, proportions are formed by comparing two equal ratios. So, if we know that two ratios are equal, we can use proportions to solve for unknown values.

How can percents be converted to fractions or decimals?

To convert a percent to a fraction, you can divide the percent by 100 and simplify the resulting fraction. For example, to convert 75% to a fraction, you would divide 75 by 100, which equals 0.75. Then, you can simplify 0.75 to 3/4. To convert a percent to a decimal, you can simply move the decimal point two places to the left. For example, 75% would become 0.75 as a decimal.

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