## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 7 - Section 7.1 - Systems of Linear Equations in Two Variables - Exercise Set - Page 823: 109

#### 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.

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