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

Answer:

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

Step-by-step 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, $\frac{1}{3}$.

Proportion of guests who chose chicken is, $\frac{5}{12}$.

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)

                        $=1-\frac{1}{3}-\frac{5}{12}$

                        $=\frac{12-4-5}{12}$

                        $=\frac{3}{12}\\\\=\frac{1}{4}$

So, the proportion of guests who chose vegetarian was $\frac{1}{4}$.

It is also provided that the number of guests who chose vegetarian was 69, i.e. $\frac{1}{4}$ of N = 69.

Compute the value of N as follows:

$\frac{1}{4}\times N=69$

     $N=69\times 4$

         $=276$

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