Math Problem?

Question

A large pizza costs $12.75; three friends decide to split one. Jack takes a third, and then Jill
takes a third of the remainder, and then Tom takes half of what’s left.
(a) How should they split the total cost so that each pays an amount proportional to what he has
eaten so far?
(b) Can they split the remaining pizza so that everyone ends up having eaten the same total
amount? If so, how?

Answer 1

Jack has had 1/3 (leaving 2/3).
Jill has 1/3 of 2/3 = 1/3 * 2/3 = 2/9 of the pizza. Now there is 2/3 - 2/9 = 4/9 left.
Tom has half of 4/9, i.e. 2/9.
So in ninths, Jack has had 3/9 of the pizza and Jill and Tom have each had 2/9; and there is 2/9 left.

(a) The total amount eaten so far is 7/9. So of the amount eaten, Jack has had (3/9) / (7/9) = 3/7, and Jill and Tom have each had 2/7. So Jack should pay 3/7 of $12.75 = $5.46 and the others should each pay 2/7 of $12.75 = $3.64. Due to rounding this is one cent short, so make Jack's payment $5.47.

(b) Yes. Jack has had exactly his share already; Jill and Tom each need to have half of the remaining pizza. (Recall they've had 2/9 each and there is 2/9 left, so they each need to have 1/9 more to get up to their 1/3 share; that 1/9 is 1/2 of the remaining amount.)

Answer 2

(a) Jack takes a third, so he's paying a third of $12.75, i.e. $12.75/3 = $4.25. The remainder would be $12.75-$4.25 = $8.50. Jill takes a third, meaning $8.50/3 = $2.83 and the remainder is $8.50-$2.83 = $5.67. Tom takes half, so he should pay $5.67/2 = $2.83.

(b) The remaining pizza costs $2.83, divided by the total amount $12.75, it's actually 2/9 of the entire pizza. So Jack took 1/3 or 3/9 of the pizza, Jill took 1/3 of the remaining, i.e. 1/3 x 2/3 = 2/9. Tom took 1/2 x 4/9 = 2/9. The remaining pizza is of course, 1-(3/9)-(2/9)-(2/9) = (2/9). Therefore Jill and Tom will have to split the remaining pizza to two, so that they get 1/9 each, which means in the end everyone will get 3/9 or 1/3 pizzas each.

First time answering.. I hope this helps...

Answer 3

total cost = 12.75. the first one takes 12.75*1/3 =4.25.
the remaining is 8.5 and then the seocnd one takes the third of that which is 8.5*1/3 = 2.833. the remaining is 5.67 and then the half from it which is 5.87*1/2 = 2.84.
the remaining is 2.84 they can split into three whic is 0.95 each. at the end of it
the first ate 5.20
the second one ate 3.74
the third one ate 3.8
the total is 5.20+3.74+3.8 = 12.75