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Word Problems/More Than 100%

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Question
QUESTION: Hello:

A fruit juice contains 120% of vitamin C.  How can more than 100% of vitamin C be contained in a fruit juice or in anything else?

I thank you for your reply.

ANSWER: The 120% refers to the RDA, or recommended dietary allowance. It means an 8-ounce serving provides you with more than the recommended amount of vitamin C. It's safe because your body eliminates the excess.

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QUESTION: Hello:

I want to thank you for the reply.

How can there be more than 100% of something in something else?  

If a classroom contains 10 students, 100% of these students is 10. Can there be 120% in the classroom?

ANSWER: You can have more than 100% of something, just as you can have more than one apple.

If a classroom contains 120% of 10 students, there are 12 students.

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QUESTION: Hello:

I want to thank you for the reply.

There are 10 students in a class and these 10 students represent 100% of the class.  Now, two more new students are added to the class.  Does the class now have 120% students?

Here's another example: Add one cup of cheerios to the bowl. Now add another 1/4 cup to the bowl.  Does it make sense to think that there is 125% of Cheerios in the bowl.

or Add 3/4 cups of Cheerios to the bowl; this is 75%. Now add another 1/4 cup to the bowl; this is 25%. Does the bowl now contain 100% of Cheerios?

I'm just guessing on these examples, but I does make some sense to me.

I thank you for your last reply.

Answer
"Does the class now have 120% students?"
No, the class does not have 120% students. Like a fraction, a percentage can represent a number by itself, or it can indicate a proportion of or comparison to another quantity.
120% by itself is the number 1.20. However, the class has 12 students, not 1.20 students!

Initially, the 10 students were 100% of the class. After the two new students join, the 12 students still represents 100% of the class, but the class size is now 120% of the original class size. Note the "of" clause. If you are using 120% as a proportion or comparison of something, you have indicate what the something is. In this case, it is the original class size.
:::::
"Does it make sense to think that there is 125% of Cheerios in the bowl."
Again, 125% by itself is just the number 1.25, which is not the number of Cheerios.
The 125% is a comparison to the original amount. The bowl now contains 125% of the original amount.
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"Does the bowl now contain 100% of Cheerios?"
No, it contains 1 cup of Cheerios, which is considerably more than 100% = 1 Cheerio.
If the bowl is now full, you can say that that Cheerios fill 100% of the capacity of the bowl.

Janet

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Janet Yang

Expertise

Word problems are my favorite type of math questions! I would not feel comfortable answering questions that require specialized knowledge (Physics, Statistics, etc.) because I have not studied these in depth.

Experience

I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

Publications
Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language.

Education/Credentials
I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley, and a Master of Business Administration degree from The Wharton School.

Past/Present Clients
George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

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