Question

Write and solve an equation to solve the problem. Lisa is 4 centimeters taller than her friend Ian. Ian is 8 centimeters taller than Jim. Every month, their heights increase by 2 centimeters. In 4 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.

(h + 8) + (__) + 8 = ( __) + 8 + 140

Ian is __ centimeters tall now.

Answer 1

Let the actual heights of Lisa, Ian and Jim be L, I and J.

i) "Lisa is 4 centimeters taller than her friend Ian." means: L=4+I

ii) "Ian is 8 centimeters taller than Jim." means: I=8+J, thus J=I-8

so the heights of Lisa, Ian and Jim are 4+I, I and I-8, respectively.



Since their heights increase by 2 cm, in 4 months, their heights increase 2 cm*4 = 8 cm.

Thus, after 4 months the heights of Lisa, Ian and Jim become:

4+I +8, I+8 and I-8+8 that is I + 12, I+8, I.


In 4 months, "the sum of Ian's and Jim's heights will be 140 centimeters more than Lisa's height. " mean:

(I+8)+I=140+(I+12)

2I+8=152+I

I=152-8=144


This solution made use of writing all the ages in terms of Ians current age.