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 proportionately 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 old would Ian have to be to get 1/4 of the cake? 1/3 of the cake? and 1/3 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.