Question

Lisa is 6 centimeters taller than her friend Ian. Ian is 10 centimeters taller than Jim. Every month, their heights increase by 2 centimeters. In 5 months, the sum of Ian's and Jim's heights will be 140 centimeters more than Lisa's height. How tall is Ian now? Let h be Ian's height today in centimeters.

Answer 1

Lan is 146 centimeters tall now.

Explanation

Let, Lan's current height is $h$ centimeters

As Lisa is 6 centimeters taller than Lan and Lan is 10 centimeters taller than Jim, so Lisa's current height = $(h+6)$ centimeters and Jim's current height = $(h-10)$ centimeters.

Every month, their heights increase by 2 centimeters.

So, after 5 months.....

Lan's height = $h+(2*5)=(h+10)$ centimeters,

Lisa's height = $(h+6)+(2*5)= (h+16)$ centimeters and

Jim's height = $(h-10)+(2*5)= h$ 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....

$(h+10)+h= (h+16)+140\\ \\ 2h+10=h+156\\ \\ 2h-h=156-10\\ \\ h=146$

So, the current height of Lan is 146 centimeters.