Lan is 146 centimeters tall now.
Explanation
Let, Lan's current height is [tex]h[/tex] centimeters
As Lisa is 6 centimeters taller than Lan and Lan is 10 centimeters taller than Jim, so Lisa's current height = [tex](h+6)[/tex] centimeters and Jim's current height = [tex](h-10)[/tex] centimeters.
Every month, their heights increase by 2 centimeters.
So, after 5 months.....
Lan's height = [tex]h+(2*5)=(h+10)[/tex] centimeters,
Lisa's height = [tex](h+6)+(2*5)= (h+16)[/tex] centimeters and
Jim's height = [tex](h-10)+(2*5)= h[/tex] centimeters
Given that, the sum of Ian's and Jim's heights will be 140 centimeters more than Lisa's height in 5 months. So the equation will be....
[tex](h+10)+h= (h+16)+140\\ \\ 2h+10=h+156\\ \\ 2h-h=156-10\\ \\ h=146[/tex]
So, the current height of Lan is 146 centimeters.
