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#preppingformymathcountsentryexam

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Okay, I went online and found a bunch of problems, but the ones idk/unshure , I'm posting here.

In a survey of 100 readers, all of whom liked fiction and/or non-fiction, three times as many people reported liking fiction as those who reported liking non-fiction. Of those surveyed, eight liked both fiction and non-fiction. How many people reported liking non-fiction?

For this one, I started drawing a Venn diagram then got confused...

Is my approach wrong?

Nov 9, 2019

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A Venn diagram is a good way to visualize these kind of problems, but if you get more familiar with the concept and how you can manipulate the numbers, it will be way easier than drawing out a Venn diagram. Out of all 100 people, 8 people liked both non fiction and fiction. Then, it tells us three times as many people like fiction over nonfiction. Consider nonfiction to be x.

3x like fiction and x and non fiction. We also have to look at the 8 people who like both. They are included in the people who like fiction and non fiction. In order to get an accurate response... you have to do the subtract the 8 out of the total.

FICTION - 8 + NONFICTION - 8 + 8 = TOTAL

3x - 8 + x - 8 + 8 = 100

4x - 8 = 100

4x = 108

x = 27

Since we said was non-fiction, 27 people reported liking non-fiction.

Nov 9, 2019
edited by mathleteig  Nov 9, 2019
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Thank you so much!

But why do you have to subtract 8 from both?

Cant, you just subtract one 8 and leave the rest alone?

tommarvoloriddle  Nov 9, 2019
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Go back to that Venn diagram.

It would have a place for FICTION, a place for NONFICTION, and then an intersection. We have to subtract eight from both because 8 people like both. If they like both, that means they are included in the place where people like fiction, in the place where people like nonfiction, and the intersection. We don't want this to be counted three times. Instead, we subtract 8 from both main quantities and just leave the thing that is common. If you haven't already, you should look at the basics of sets. It kind of gets into this topic once you learn the main idea.

Nov 10, 2019
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I hope you enjoyed getting schooled by a seventh grader! I'm just kidding. I wish you the best of luck for your MATHCOUNTS entry exam.

Nov 10, 2019
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I'm supposed to be in 5th grade...

tommarvoloriddle  Nov 10, 2019
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Its ok lol

your math skills will increase as you grow up.

CalculatorUser  Nov 10, 2019
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And YOU will get kicked out of AOPS for TROLLING FTW with your SKILLS

tommarvoloriddle  Nov 10, 2019
edited by tommarvoloriddle  Nov 10, 2019
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Lol i have no skills my rating is a lowly 1217.

You START at 1200 lol.

CalculatorUser  Nov 10, 2019
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T-T

When an 11-year-old is at 1150

tommarvoloriddle  Nov 10, 2019
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wow that is gud.

I at first dropped all the way to a 1017, then I worked slowly to a 1217.

CalculatorUser  Nov 10, 2019
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I was at 1003 once...

tommarvoloriddle  Nov 13, 2019
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I didn't know how to play AoPS FTW

tommarvoloriddle  Nov 13, 2019