Question

How tall is the table?

Answer 1

Hint: We first assume the height of the star, the circle and the table as variables. We try to find the mathematical expression of the given conditions from the images and form the equations. We add those equations and simplify to find the table’s height.

Complete step by step solution:
From the given image we have to find the height of the table. The two different images will give us two different equations.
We first assume the height of the star, the circle and the table as $c$, $t$ and $x$ respectively.
For the first part of the image, we get that if we add the star’s height and subtract the circle’s height from the table’s height, we will get 170.
The mathematical expression will be $x+c-t=170....(i)$.
Similarly, for the second part of the image, we get that if we subtract the star’s height and add the circle’s height from the table’s height, we will get 130.
The mathematical expression will be $x-c+t=130....(ii)$.
We have two equations and we add them to find the table’s height.
Therefore, $\left( x+c-t \right)+\left( x-c+t \right)=170+130$.
Simplifying we get
$\begin{align}
  & \left( x+c-t \right)+\left( x-c+t \right)=170+130 \\
 & \Rightarrow x+c-t+x-c+t=170+130 \\
 & \Rightarrow 2x=300 \\
 & \Rightarrow x=\dfrac{300}{2}=150 \\
\end{align}$
The height of the table is 150 cm.

Note: We need to remember that we can also express that the total height of all things is not similar. As in different cases one shape’s height is already included in the table’s height. So, we have to be careful calculating the total height.