Chapter 3.4, Problem 22P

A family decides to rent a boat for the day while on vacation. The boat’s rental rate is $ 500 for the first two hours and $ 50 for each additional half hour. Suppose the family can spend $ 700 for the boat. What inequality represents the number of hours for which they can rent the boat?

To determine

To find: the inequality that represents the number of hours for which they can rent the boat.

Answer to Problem 22P

  $2\le x\le 4$

Explanation of Solution

Given information: A family decides to rent a boat for the day while on vacation. The boat’s rental rate is $500 for the first two hours and $50 for each additional half hour. The family can spend $700 for the boat.

Calculation:

Let x be the number of hours for which they can rent the boat, where $x\ge 2$

The boat’s rental rate is $500 for the first two hours and $50 for each additional half hour.

Therefore, rent of first two hours is $500 and rent for ( x- 2) hours is $100( x- 2)

Total rent =500+100( x- 2)

The family can spend $700 for the boat.

Therefore,

  $\begin{array}{l}500+100\left(x-2\right)\le 700\\ 100\left(x-2\right)\le 700-500\\ 100x-200\le 200\\ 100x\le 400\\ x\le 4\end{array}$

Therefore, the inequality that represents the number of hours for which they can rent the boat is

  $2\le x\le 4$