Question

Joe organised a large wedding.

Guests had to choose there meal from beef, chicken or vegetarian.

1/3 of the guests chose beef

5/12 of the guests chose chicken

69 of the guests chose vegetarian.

How many guests were at the wedding?

Answer 1

The total number of guests that were at the wedding was 276.

Explanation:

Let the total number of guests at the wedding be, N.

The meal options are:

Beef, Chicken and Vegetarian.

It is provided that:

Proportion of guests who chose beef is,
`(1)/(3)`.

Proportion of guests who chose chicken is,
`(5)/(12)`.

According to the laws of probability, the sum of the probabilities of all the events of a sample space is 1.

Then the sum of probability of guests selecting beef, chicken or vegetarian should also be 1.

Compute the proportion of guests who chose vegetarian as follows:

P (Vegetarian) = 1 - P (Beef) - P (Chicken)

`=1-(1)/(3)-(5)/(12)`

`=(12-4-5)/(12)`

`=(3)/(12)\\\\=(1)/(4)`

So, the proportion of guests who chose vegetarian was
`(1)/(4)`.

It is also provided that the number of guests who chose vegetarian was 69, i.e.
`(1)/(4)` of N = 69.

Compute the value of N as follows:

`(1)/(4)* N=69`

`N=69* 4`

`=276`

Thus, the total number of guests that were at the wedding was 276.