Chapter 4.5, Problem 2P

a.

To determine

To find: a function rule for the total cost for n days of boarding plus bath. And how much does 10 days stay cost.

Answer to Problem 2P

The rule is $15n+12$

The costs to stay a dog are $162 for 10 days.

Explanation of Solution

Given information:

A kennel charges $15 per day to board dogs. And each dog has a flea bath that costs $12.

Multiply the kennel charges and cost for n days of boarding,

  $15\times n=15n$

And each dog has flea bath then add $12 with $15n$ .

  $15n+12$

This is the required function rule.

Now find the costs of a 10 days stay, substitute 10 for n in calculated rule.

  $\begin{array}{l}15\left(10\right)+12=150+12\\ =162\end{array}$

Therefore the costs to stay a dog are $162 for 10 days.

b.

To determine

To Explain: A 5-days stay cost as much as a 10-day stay

Answer to Problem 2P

The 5-day cost is not half as much as 10 day cost.

Explanation of Solution

Given information:

A kennel charges $15 per day to board dogs. And each dog has a flea bath that costs $12.

In the part (a) the value of costs to stay a dog are $162 for 10 days.

And the value of costs to stay a dog for 5 days is,

  $\begin{array}{l}15\left(5\right)+12=75+12\\ =87\end{array}$

Therefore when compare with 10 days; find half the value of 10 days,

  $\frac{1}{2}\left(162\right)=81$

Which are not equal to 5 days cost, therefore a 5-day cost is not half as much as 10 day cost.