Chapter 6.1, Problem 45STP

a.

To determine

To calculate:System of equation that models the situation.

Answer to Problem 45STP

  $\begin{array}{l}y=5+2.5x\\ y=20\end{array}$

Explanation of Solution

Given information:

garage	Flat fee	Hourly fee
A	$\$5$	$\$2.50$
B	$\$20$	$\$0$

Calculation:

Let’s say $y$ is the total fee paid and $x$ is the hour for which car is parked.

Now, the first garage will take,

  $\therefore y=5+2.5x$

Now, the second garage will take,

  $\therefore y=20$

b.

To determine

To calculate:Hours of parking which would cost the same parking in either garage.

Answer to Problem 45STP

  $6$ hours.

Explanation of Solution

Given information:

garage	Flat fee	Hourly fee
A	$\$5$	$\$2.50$
B	$\$20$	$\$0$

Calculation:

  $y=5+2.5x$ ….(i)

  $y=20$ ….(ii)

Substitute $y$ from equation (ii) to equation (i)

  $\therefore 20=5+2.5x$

  $\therefore x=6$

c.

To determine

Selection of garage if you need to park for $3$h.

Answer to Problem 45STP

  $A$ , as it will cost less.

Explanation of Solution

Given information:

garage	Flat fee	Hourly fee
A	$\$5$	$\$2.50$
B	$\$20$	$\$0$

Calculation:

For $3$ h, garage $A$ will cost,

  $\therefore y=5+2.5x=5+2.5\cdot 3=\$12.5$

And the garage $B$ will cost,

  $\therefore y=\$20$

Therefore, garage $A$ is cheap.