Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 7 - Section 7.1 - Systems of Linear Equations in Two Variables - Exercise Set - Page 822: 88


The restaurant should should purchase $6$ two-seat tables and $11$ four-seat tables.

Work Step by Step

Let us assume x to be the number of two-seat tables and y to be the number of four-seat tables. The provided data can be represented in the form of equations as follows: $4x+2y=56$ (I) $x+y=17$ (II) Solve for x in the second equation to obtain its value in terms of y: $\begin{align} & x+y=17 \\ & x=17-y \end{align}$ Put the value of $x$ from the second equation in the first equation: $\begin{align} & 4x+2y=56 \\ & 4\cdot \left( 17-y \right)+2y=56 \end{align}$ Simplify: $\begin{align} & 68-4y+2y=56 \\ & 68-56=2y \\ & 12=2y \end{align}$ And divide by $2$ on both sides $\begin{align} & y=6 \\ & x=17-y \\ \end{align}$ Put the value $y=6$ in $x=17-y$: $\begin{align} & x=17-6 \\ & x=11 \\ \end{align}$ Hence, the number of four-seat tables is $11$ and the number of two-seat tables is $6$.
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