## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 7 - Review Exercises - Page 877: 9

#### Answer

The hotel cost per day is $\$80$and the car rental charge per day is$\$60$.

#### Work Step by Step

We assume the cost per day for the hotel is x and the cost per day for the car is y. According to the statement, package $1$ costs $\$360$and includes$3$days at the hotel and a rental car for$2$days. Thus, the equation becomes:$3x+2y=360$Which can be written as:$ y=\frac{1}{2}\left( 360-3x \right)$Package$2$costs$\$500$ and includes $4$ days at the hotel and a rental car for $3$ days So, the equation becomes: $4x+3y=500$ Putting the value of $y=\frac{1}{2}\left( 360-3x \right)$ in the equation $4x+3y=500$ gives: \begin{align} & 4x+\frac{3}{2}\left( 360-3x \right)=500 \\ & 8x+1080-9x=1000 \\ & x=80 \end{align} Now, substitute the value of x in the equation $y=\frac{1}{2}\left( 360-3x \right)$ as given below: \begin{align} & y=\frac{1}{2}\left( 360-3\times 80 \right) \\ & =60 \end{align} Hence, the hotel cost per day is $\$80$and the car rental charge per day is$\$60$.

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