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: 86

Answer

43% is the percentage of the students who sleep between 5 and 7 hours and 2% is the percentage of students who sleep between 9 and 11 hours.

Work Step by Step

Let us assume x to be the number of students who sleep between $5\,\,\text{ and }\,\,7$ hours and y to be the number of students who sleep between $9\,\,\text{ and }\,\,11$ hours.. The provided data can be represented in the form of the system of equations as follows: $x+y=45$ (I) $x-y=41$ (II) Now add both of the equations above: $\begin{align} & \left( x+y \right)+\left( x-y \right)=\left( 41+45 \right) \\ & 2x=86 \\ & x=43 \end{align}$ Put the value of x in (II): $\begin{align} & x-y=41 \\ & 43-y=41 \\ & y=2 \end{align}$ Hence, the percentage of the students who sleep between 5 and 7 hours is 43% and the percentage of students who sleep between 9 and 11 hours is 2%.
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