The cast of a play had a party. The drama teacher served 20 cookies and 40 carrot sticks as refreshments. Each cast member ate the same number of whole cookies and the same number of whole carrot sticks. Nothing was left over. The drama teacher did not eat. How many cast members might have been at the party? Explain.

people

surely 20 is a possibility

whats the answer

To solve this problem, we can set up an equation based on the given information.

Let's assume that there were 'x' cast members at the party.
We know that each cast member ate the same number of whole cookies and the same number of whole carrot sticks.
So, let's say each cast member ate 'c' whole cookies and 's' whole carrot sticks.

The drama teacher served 20 cookies, which means the total number of cookies consumed by the cast members would be 'x * c'. Similarly, the total number of carrot sticks consumed would be 'x * s'.

We are given that 20 cookies and 40 carrot sticks were served and nothing was left over. Therefore, we can set up the equation:

x * c = 20 (equation 1)
x * s = 40 (equation 2)

To find the number of cast members at the party, we need to find a value of 'x' for which both equations 1 and 2 are satisfied.

One possible solution is x = 4, c = 5, s = 10:
4 * 5 = 20 (equation 1 is satisfied)
4 * 10 = 40 (equation 2 is satisfied)

So, there might have been 4 cast members at the party in this case.