Answer
The number of squares which can be made is 4 and the number of hexagons which can be made is 8.
Work Step by Step
Let us assume the number of squares to be made to be x. Also, let the number of hexagons to be made to be y
Therefore, for the square, the used members are 1 of the band group and 4 of the pom- pom squad.
And for the hexagon, the used members are 6 of the band group and 1 of the pom-pom squad.
Therefore, the total number of band members is:
$x+6y=52$ (I)
And the pom-pom squad is:
$4x+y=24$ (II)
Then, multiply equation (II) with 6 and apply the elimination method to (I) and (II):
$x+6y=52$ (I)
$4x+y=24$ (II)
Therefore,
$x+6y=52$
$24x+6y=144$
$-23x=-92$
$\begin{align}
& x=4 \\
& x+6y=52 \\
& x=4 \\
& 4+6y=52
\end{align}$
$\begin{align}
& 6y=48 \\
& y=8
\end{align}$
Thus, the number of squares which can be made is 4 and the number of hexagons which can be made is 8.
