how many guests were present at a dinner if every two guest shared a bowl of rice, every three guests shared a bowl of broth, every four guests shared a bowl of fow, and 65 bowls were used together.

x/2+x/3+x/4=65

multliply both sides by 12
6x+4x+3x=65*12
13x=....

60 guest were present at dinner. Is this correct?

To determine the number of guests present at the dinner, we need to find a common factor among the given sharing conditions.

Let's break down the information:

1. Every two guests shared a bowl of rice.
2. Every three guests shared a bowl of broth.
3. Every four guests shared a bowl of fowl.
4. A total of 65 bowls were used together.

To find the common factor among the sharing conditions, we need to find the least common multiple (LCM) of 2, 3, and 4.

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ...

From the multiples listed above, we can observe that the least common multiple of 2, 3, and 4 is 12.

Now, we know that every 12 guests will share a bowl of rice, broth, and fowl. Therefore, we can calculate the number of guests by dividing the total number of bowls used (65) by the number of bowls shared among 12 guests:

Number of guests = Total bowls used / Bowls shared among 12 guests
Number of guests = 65 / 12
Number of guests ≈ 5.42

Since it's not possible to have a fraction of a guest, we need to round the number to the nearest whole number. Thus, the number of guests present at the dinner is approximately 5.