Chapter 3.4, Problem 24HP

To determine

To find: The number of red triangle that will balance one green circle.

Answer to Problem 24HP

The 5 red triangles will balance one green circle

Explanation of Solution

Given information :

The system of equation is written as follows:

  $\begin{array}{l}t+c=s\\ p+t=c\\ 2s=3p\end{array}$

Calculation :

Consider t represents a triangle, c represents a circle, s represents a square and p pentagon.

The system of equation is written as follows:

  $\begin{array}{l}t+c=s\\ p+t=c\\ 2s=3p\end{array}$

Put $c=p+t$ in equation one as follows:

  $\begin{array}{r}\hfill t+c=s\\ \hfill t+p+t=s\\ \hfill 2t+p=s\end{array}$

Put $s=\frac{3}{2}p$ in $2t+p=s$ as follows:

  $\begin{array}{l}2t+p=\frac{3}{2}p\\ 4t+2p=3p\\ 4t=p\end{array}$

Put $4t=p$ in equation two as follows:

  $4t+t=c$

  $5t=c$

Therefore, the 5 red triangles will balance one green circle.