#### 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.