How many hotdogs did each male guest eat?

Question

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?

Answer 1

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 $4$ .

Answer 2

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.

Answer 3

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 $\color{red}4$.