Chapter 4.2, Problem 31PPS

a.

To determine

To define the variables and to write an equation in standard form.

Answer to Problem 31PPS

  $100x+150y=1200$

Explanation of Solution

Given:

Given that rental company charges $100 per hour to rent a paddle boat.

$150 per hour to rent a pontoon boat.

Total money spent is $1200.

Concept used:

Standard form of $ax+by=c.$

Calculation:

Let x be the number of hours of renting paddle boat and y be the number of hours of renting pontoon boat.

Given that rental company charges $100 per hour to rent a paddle boat and $150 per hour to rent pontoon boat.

  $\Rightarrow 100x+150y=1200$

Conclusion:

Therefore, the standard equation in $100x+150y=1200$

b.

To determine

To graph the given equation in subpart (a)

Explanation of Solution

Given:

Given that rental company charges $100 per hour to rent a paddle boat.

$150 per hour to rent a pontoon boat.

From subpart (a),

  $100x+150y=1200$

Calculation for graph:

  $\begin{array}{l}100x+150y=1200\\ \Rightarrow 150y=1200-100x\\ \Rightarrow y=\frac{1200-100x}{150}\end{array}$

x	0	1	2	3
y	8	7.33	6.66	6

Graph:

The points found can be plotted as follows:

  

Inference:

The equation in subpart (a) is plotted as above.

c.

To determine

To find the number of hours that pontoon boat is rented.

Answer to Problem 31PPS

5

Explanation of Solution

Given:

The paddle boat is rented for 6 hours.

From subpart (a),

  $100x+150y=1200$

Calculation:

Let x be the number of hours of renting paddle boat and y be the number of hours of renting pontoon boat.

  $100x+150y=1200$

Given that the paddle boat is rented for 6 hours.

  $\begin{array}{l}100x+150y=1200\\ \Rightarrow 100(6)+150y=1200\\ \Rightarrow 600+120y=1200\\ \Rightarrow 120y=600\\ \Rightarrow y=5\end{array}$

Conclusion:

Therefore, the number of hours that the pontoon boat is rented is 5 hours.