Reasoning problem: find number of party guests from....

[nikkinonanay]

A city official was monitoring the water, when he saw a woman washing dishes. He asked, "Why are there so many dishes here?" she said"there was a dinner party". He asked, "How many guests were there?", She said she didn't know, but every two guests shared one dish for rice, every three guests shared one dish for broth, every four guests shared one dish for meet. There were 65 dishes altogether. How many guests were there? :?:

 

[soroban]

Re: Reasoning problem

Hello, nikkinonanay!

A city official was monitoring the water, when he saw a woman washing dishes.
He asked, "Why are there so many dishes here?"
She said, "There was a dinner party".
He asked, "How many guests were there?".
She said she didn't know,
but every two guests shared one dish for rice,
every three guests shared one dish for broth,
every four guests shared one dish for meat.
There were 65 dishes altogether.
How many guests were there?

Let \(\displaystyle N\) = number of guests.

. . \(\displaystyle \begin{array}{c}\frac{N}{2} \text{ dishes were used for rice} \\ \\[-3mm] \frac{N}{3}\text{ dishes were used for broth} \\ \\[-3mm] \frac{N}{4} \text{ dishes were used for meat} \end{array} \quad \text{ 65 dishes were used.}\)


\(\displaystyle \text{There is our equation! }\quad\hdots\quad \frac{N}{2} + \frac{N}{3} + \frac{N}{4} \;=\;65\)

. . Go for it!