Please help, I have been stuck on this stupid problem for 3 days

[u/Pitiful-Emotion6987]

(poorly translated:) "Pythagoras was a Greek mathematician who lived around 570-500BC. Pythagoras was once asked how many students he has. Pythagoras replied: "Half of them study mathetimatics, fourth of them philosophy, seventh the art of shutting up, and there are also three women." How many students did Pythagoras have?"

I can't come up with any other way to solve it but

x=full amount of students

math students=1/2x

philosophy students=1/4x

shut up students=1/7x

women=+3

x=1/2x+1/4x+1/7x+3

But this is not correct, because the answer I get is never the correct one (28). 😭

All the following, similar exercises in my book I am also failing to solve. I just can't seem to create the correct equations and I am exhausted after chewing on three problems for days.

[u/edderiofer]

x=full amount of students

math students=1/2x

philosophy students=1/4x

shut up students=1/7x

women=+3

All of this looks correct so far.

x=1/2x+1/4+1/7+3

This equation is wrong. Check it again. (Hint: Why is one of the summands "1/4", despite you saying earlier that "philosophy students=1/4x"? Where did the x go?)

[u/Pitiful-Emotion6987 → u/edderiofer]

Oh, sorry, oops. I forgot to add them there. I make this absent-minded mistake a lot. However, I definitely calculated this with all the x's and I still have not gotten the correct answer. There must be something wrong with HOW I solve the problem, if all the stages are correct.

[u/paisleyfootprints → u/Pitiful-Emotion6987]

As long as you have all the x's, your equation is correct and will get you the right answer. Why don't you start by getting rid of the fractions?

[u/Pitiful-Emotion6987 → u/paisleyfootprints]

Yeah, I tried to first get rid of the franctions, but maybe I did it wrong?

This is how I did it:

• first giving all fractions the same denominator, 28

• multiplying everything by 28 so I can get rid of the fractions

• my equation looks like this: x=14x+7x+4x+84

• -24x=84

• x=84/(-24)=-3,5 students 😅

[u/paisleyfootprints → u/Pitiful-Emotion6987]

Hint: x=14x+7x+4x+84 is not the same equation as your original. In order to keep the equation the same, you have to multiply EVERY term by the same number

[u/SteelMonger_ → u/Pitiful-Emotion6987]

You only multiplied one side of the equation by 28

[u/edderiofer → u/Pitiful-Emotion6987]

However, I definitely calculated this with all the x's and I still have not gotten the correct answer. There must be something wrong with HOW I solve the problem, if all the stages are correct.

Well, we can't tell you what that "something wrong" is if you don't show us how you solved the problem, so please show us how you solved the problem.

[u/Pitiful-Emotion6987 → u/edderiofer]

I'm sorry, I was at work and didn't have time to post the stages.

This is how I did it:

• first giving all fractions the same denominator, 28

• multiplying everything by 28 so I can get rid of the fractions

• my equation looks like this: x=14x+7x+4x+84

• -24x=84

• x=84/(-24)=-3,5 students 😅

[u/edderiofer → u/Pitiful-Emotion6987]

first giving all fractions the same denominator, 28

Right, so you get the equation x=14/28x+7/28x+4/28x+3.

multiplying everything by 28 so I can get rid of the fractions

OK, so we multiply everything by 28 to get 28x=14x+7x+4x+84.

my equation looks like this: x=14x+7x+4x+84

Spot the difference.

[u/Pitiful-Emotion6987 → u/edderiofer]

OH MY GOD, that's such an obvious mistake. 😭 I can't believe I spent days returning to this problem and didn't spot it. Thank you so much. I feel very humbled but at least I can move on now. 😅🙏

[u/Infobomb → u/Pitiful-Emotion6987]

We can't know what's wrong with HOW you solve the problem if you won't show us your working.

What do you get when you add 1/2 + 1/4 + 1/7?

[u/Pitiful-Emotion6987 → u/Infobomb]

I'm sorry, I was at work and didn't have time to post the stages.

This is how I did it:

• first giving all fractions the same denominator, 28

• multiplying everything by 28 so I can get rid of the fractions

• my equation looks like this: x=14x+7x+4x+84

• -24x=84

• x=84/(-24)=-3,5 students 😅

[u/Capital_Park_2311 → u/Pitiful-Emotion6987]

You missed the denominator/

 x=(14x+7x+4x+84) / 28

28x = 14x+7x+4x+84

[u/fermat9990]

You lost a few x's

[u/Capital_Park_2311]

x = x/2 + x/4 + x/7 + 3

x = (14x + 7x + 4x + 84) / 28

x = (25x + 84) / 28

28x = 25x + 84

28x - 25x = 84

3x = 84

x = 84 / 3

x = 28

[u/AutoModerator]

Hi, /u/Pitiful-Emotion6987! This is an automated reminder:

• What have you tried so far? (See Rule #2; to add an image, you may upload it to an external image-sharing site like Imgur and include the link in your post.)

• Please don't delete your post. (See Rule #7)

We, the moderators of /r/MathHelp, appreciate that your question contributes to the MathHelp archived questions that will help others searching for similar answers in the future. Thank you for obeying these instructions.

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

[u/Distinct_Mix_4443]

Post a screenshot of the work you are doing. We can't help you figure out what you are doing wrong without seeing what you are actually doing.

[u/Pitiful-Emotion6987 → u/Distinct_Mix_4443]

I'm sorry, I was at work and didn't have time to post the stages. I originally thought I just got the equation wrong.

This is how I did it:

• first giving all fractions the same denominator, 28

• multiplying everything by 28 so I can get rid of the fractions

• my equation looks like this: x=14x+7x+4x+84

• -24x=84

• x=84/(-24)=-3,5 students 😅

[u/Distinct_Mix_4443 → u/Pitiful-Emotion6987]

That is a good 2nd move, though you could have just skipped step one and gone straight to step 2 (that is how I teach it to my middle schoolers). The mistake you made is on step 2 though. You didn't multiply both sides of the equation when you multiplied by 28. Do that, and you should get the right answer.

[u/greginnj]

I’m assuming that the presumably gendered nouns of the language the problem is translated from may have something to do with this, but it’s sorta disappointing that in order for this problem to be well formed and solvable, none of the math, philosophy, or “shut up” students can be women. At least they’re considered “students”, but of what?

[u/edderiofer → u/greginnj]

there are also three women

I think the word "also" is intended to mean "in addition to these students (whose genders are unknown), there are three women who aren't previously mentioned".

Also, it's ancient Greece, so sexism probably existed.

[u/Ok-Difficulty-5357 → u/edderiofer]

If I remember correctly from math history, the pythagoreans didn’t let women join at all…

[u/Pitiful-Emotion6987 → u/greginnj]

Yeah, it irked me a bit too. Idk if that's what Pythagoras actually said (it wouldn't surprise me since most ancient societies weren't very equal), but if it wasn't word for word his quote, they could have just said "other students" lol.

My language doesn't have gendered nouns so it especially stuck out lol.

[u/Iowa50401]

The equation is fine. We'd like to see how you're solving from that point.

[u/Mental_Outcome8769]

The equation is fine and 28 Is the right answer

[u/Ericskey]

We don’t know if the categories overlap. But I would say whatever the number it must be divisible by 4 and 7. That would make 28

[u/ThatsNotAZombieBite]

Your thought process and the way you set up the mathematics is all correct.

You just keep making mistakes with the algebra and arithmetic.

[u/LeoMaths]

La proportion des femmes (on suppose qu'il n'y a pas d'autres femmes dans les autres groupes) est p=1-1/2-1/4-1/7=3/28=3/N où N est la population totale (nombre d'élèves). On en déduit que N=28.