Precalculus (6th Edition) Blitzer

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%.