Question

Can someone help with the equation for this?? Jon has a handful of pizzas. Someone takes 1/2 of them plus 1/2 of one pizza. Someone else comes and takes 1/2 of what's left plus 1/2 a pizza. A third person takes 1/2 of what's left plus 1/2 pizza. All pizzas is gone. How many did they start with?

Answer 1

start with a pizzas

start with a pizzas
after one division, two people have

(a-1)/2 and (a+1)/2 per person

after the next division, the holdings are

(a-1)/2 (a-1)/4 (a+3)/4

after the third division, the holdings are

(a-1)/2 (a-1)/4 (a-1)/8 (a+7)/8

Looks like 8 pizzas to start. At each step of the way, the amount of pizza held by each person is:

8
7/2 9/2
7/2 7/4 11/4
7/2 7/4 7/8 15/8

Now, if you want each person to have a whole number of pizzas, then start out with

17
8 9
8 4 5
8 4 2 3

If there are n people, start out with 2^n + 1 pizzas and everyone gets whole pizzas.