The queen asked her cook how many guests had attended a recent banquet. “I do not know, my lady” he said, “but every two guests shared a plate of fruit between them, every three used a bowl of broth among them, and every four shared a platter of beef. I used 65 serving dishes in all”. The queen was able to compute the number of guests using this information. How many guest were there?

Question

The queen asked her cook how many guests had attended a recent banquet. “I do not know, my lady” he said, “but every two guests shared a plate of fruit between them, every three used a bowl of broth among them, and every four shared a platter of beef. I used 65 serving dishes in all”. The queen was able to compute the number of guests using this information. How many guest were there?

please explain how you got it

Answer 1

Here is Steve's answer:

g/2 + g/3 + g/4 = 65
13g/12 = 65
g = 60

In the second line, he found the common denominator -- which is 12. Then he converted to equivalent fractions. : g/2 = 6g/12
g/3 = 4g/12
g/4 = 3g/12

Answer 2

O ok thanks i reaally appreciate it

Answer 3

You're welcome.

Answer 4

To find the number of guests who attended the banquet, we need to solve the problem step by step.

Let's assume the total number of guests as 'x'.

According to the information given, every two guests shared a plate of fruit, every three used a bowl of broth, and every four shared a platter of beef.

To find the number of plates of fruit used, we can divide the total number of guests (x) by 2. Since we have '65' serving dishes in total, we have:

x/2 = number of plates of fruit

Similarly, to find the number of bowls of broth used, we divide the total number of guests (x) by 3:

x/3 = number of bowls of broth

And, to find the number of platters of beef used, we divide the total number of guests (x) by 4:

x/4 = number of platters of beef

Now, we know that the total number of serving dishes used is 65. So, we can set up the equation:

number of plates of fruit + number of bowls of broth + number of platters of beef = 65

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

To solve this equation, we can multiply both sides by the least common multiple (LCM) of 2, 3, and 4, which is 12:

12 * (x/2) + 12 * (x/3) + 12 * (x/4) = 12 * 65

Simplifying the equation gives us:

6x + 4x + 3x = 780

13x = 780

Dividing both sides by 13, we find:

x = 780/13

Therefore, the number of guests at the banquet is approximately 60.

So, based on the information provided, there were about 60 guests at the banquet.