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Nina cooked 121 hotdogs for the Christmas party. There were 16 male and 18 female guests. Each male guest ate 1 more hotdog than each female guest. Each of the female guests, including Nina, ate equal number of hotdogs. How many hotdogs did each male guest eat?

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closed as off-topic by TheGeekGreek, iadvd, C. Falcon, Namaste, user223391 Feb 10 '17 at 1:47

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  • 2
    $\begingroup$ The wording could be improved since Nina is not a guest. $\endgroup$ – N. F. Taussig Feb 9 '17 at 11:43
  • $\begingroup$ I really have no idea, can you at least give me a hint? @N.F.Taussig? $\endgroup$ – Hnry Feb 9 '17 at 11:50
  • $\begingroup$ Let $x$ be the number of hotdogs each male guest ate. Now work out all the relevant numbers in terms of $x$, get an equation, and solve it. $\endgroup$ – Gerry Myerson Feb 9 '17 at 11:53
  • $\begingroup$ I guess I wasn't counted, since I ate one less of hotdogs than Nina did. $\endgroup$ – Namaste Feb 10 '17 at 1:30
  • $\begingroup$ That's an alternative fact, btw. $\endgroup$ – Namaste Feb 10 '17 at 1:31
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Let $x$ be the number of hotdogs that one female guest ate . Then we have :

$$16(x+1)+18x+x=121$$ $$16x +16+19x=121$$ $$35x=121-16$$ $$35x=105$$ $$x=3$$

So number of hotdogs that each male guest ate is $4$ .

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Let each female eat x hotdogs.

We have 19 females including Nina.

So hotdogs eaten by females = 19x

Each male eat 1 more hotdog than by female. So hotdog eaten by each male = (x + 1)

And we have 16 male so total hotdogs eaten by them = 16(x + 1)

Total hotdogs eaten by male and female = 121

19x + 16(x + 1) = 121

19x + 16x + 16 = 121

35x = 121 - 16

35x = 105

x = 3

So each female eat 3 hotdogs.

And each male eat 4 hotdogs.

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  • $\begingroup$ Any doubt you can ask. $\endgroup$ – Kanwaljit Singh Feb 9 '17 at 12:59
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Assume all hotdogs are eaten, i.e. number of hotdogs eaten is $121$.

If each of $16$ male guests did not eat the $1$ hotdog more than each of the female guests,

  • the total number of hotdogs eaten would have been $121-16=105$
  • all guests (including Nina) would have eaten the same number of hotdogs each which is $105\div 35=3$

However, since each male guest ate $1$ more, the number of hotdogs eaten by each male guest is $\color{red}4$.

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