Problema Solution
Ian and his father share a birthday, so they always share a cake. When Ian was 6 years old, his father made an interesting proposal: "since I'm 30 years old and your only 6, I should get 30/36 of the cake, and you should get 6/36 of the cake, or 1/6 of the cake. "
Ian thought about the idea and said, "so next year I would get 7/38 of the cake, right?"
his father answered "yes, that's the idea. Every year we can split it according to our ages."
how long will it be before ian gets 1/4 of the cake? 1/3 of the cake? 1/2 of the cake?
Answer provided by our tutors
let
x = the age of Ian
x + (30 - 6) = x + 24 the age of Ian's father
How old would Ian have to be to get 1/4 of the cake?
x/(x + x + 24) = 1/4
by solving the equation we find
x = 12
click here to see the step by step solution of the equation
indeed when Ian is 12 years old his father will be 12 + 24 = 36
Ian will get 12/(36 + 12) = 12/48 = 1/4 of the cake
Ian has to be 12 years old to get 1/4 of the cake.
How old would Ian have to be to get 1/3 of the cake?
x/(x + x + 24) = 1/3
by solving the equation we find
x = 24
click here to see the step by step solution of the equation
indeed when Ian is 24 his father will be 24 + 24 = 48
Ian will get 24/(24 + 48) = 24/72 = 1/3 of the cake
Ian has to be 24 years old to get 1/3 of the cake.
How old would Ian have to be to get 1/2 of the cake?
x/(x + x + 24) = 1/2
by solving the equation we get contradiction (the equation has no solutions) follows Ian will never get half of the cake.
click here to see the step by step solution of the equation