Problema Solution
Ian and his father share a birthday. When Ian was 6 years old, his father made a 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 proportionally 1/6 of the cake. How old would Ian be before he got 1/2 of the cake?
Answer provided by our tutors
when Ian is 6 years old his father is 24 years old thus the age difference between them is 24
let x = the age of Ian then x + 24 will be the age of his father
How old would Ian have to be to get 1/2 of the cake?
x/(x + x + 24) = 1/2
x/(2x + 24) = 1/2 multiply both sides by 2
x/(x + 12) = 1 multiply both sides by (x + 12)
x = x + 12
0 = 12
this is a contradiction thus we can conclude that Ian will never get 1/2 of the cake.