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 you’re only 6, I should get 30/36 of the cake, and you should get 6/36 . 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 ¼ of the cake? 1/3 of the cake? ½ 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 follows Ian will never get half of the cake.
click here to see the step by step solution of the equation