Chapter 8.1, Problem 59PPS

a.

To determine

To determine the polynomial expression that represents the cost of renting a car for $m$ miles.

Answer to Problem 59PPS

$ $(25+0.35m)$

Explanation of Solution

Given:

Cost of renting a car for a day is $ $25$

Cost per mile is $ $0.35$

Calculation:

Let’s consider miles as $m$ .

So, cost per day can be represented by,

Cost per day $=\$(25+0.35m)$

Conclusion:

Therefore, the polynomial expression that represents the cost of renting a car for $m$ miles is

  $\$(25+0.35m)$ .

b.

To determine

To determine the cost to rent a car driven $145$ miles a day.

Answer to Problem 59PPS

  $\$75.75$

Explanation of Solution

Given:

Cost of renting a car for a day is $ $25$

Cost per mile is $ $0.35$

Car driven is $145$ miles a day

Calculation:

Car driven is $145$ miles a day.

So, cost per day $=\$(25+0.35m)$

Here $m=145$ miles

So, cost to rent a car driven for $145$ miles a day can be represented by,

  $\Rightarrow$ Cost per day $=\$(25+0.35\times 145)$

  $\Rightarrow$ Cost per day $=\$75.75$

Conclusion:

Therefore, the cost to rent a car driven $145$ miles a day is $\$75.75$ .

c.

To determine

To determine the cost to rent a car driven $105$ miles each day for four days.

Answer to Problem 59PPS

  $\$247$

Explanation of Solution

Given:

Cost of renting a car for a day is $ $25$

Cost per mile is $ $0.35$

Car driven $105$ miles each day for four days

Calculation:

At first cost to rent a car driven $105$ miles for a single day is,

  $\Rightarrow$ Cost per day $=\$(25+0.35m)$

Here $m=105$ miles

So, cost to rent a car driven for $105$ miles a day can be represented by,

  $\Rightarrow$ Cost per day $=\$(25+0.35\times 105)$

  $\Rightarrow$ Cost per day $=\$61.75$

Now, cost to rent a car driven for $105$ miles each day for four days is,

  $\Rightarrow$ Cost for four day $=4\times \$61.75$

  $\Rightarrow$ Cost for four day $=\$247$

Conclusion:

Therefore, the cost to rent a car driven $105$ miles each day for four days is $\$247.$

d.

To determine

To determine the cost to rent a car driven $220$ miles each day for seven days.

Answer to Problem 59PPS

  $\$714$

Explanation of Solution

Given:

Cost of renting a car for a day is $ $25$

Cost per mile is $ $0.35$

Car driven $220$ miles each day for seven days

Calculation:

At first cost to rent a car driven $220$ miles for a single day is,

  $\Rightarrow$ Cost per day $=\$(25+0.35m)$

Here $m=220$ miles

So, cost to rent a car driven for $105$ miles a day can be represented by,

  $\Rightarrow$ Cost per day $=\$(25+0.35\times 220)$

  $\Rightarrow$ Cost per day $=\$102$

Now, cost to rent a car driven for $220$ miles each day for seven days is,

  $\Rightarrow$ Cost for seven day $=7\times \$102$

  $\Rightarrow$ Cost for seven day $=\$714$

Conclusion:

Therefore, the cost to rent a car driven $220$ miles each day for seven days is $\$714.$