Chapter 3.4, Problem 14E

To determine

To find: Number of hours for which will both rafting companies charge the same amount.

Answer to Problem 14E

Number of hours at which both total costs will be equal is 5 hours.

Explanation of Solution

Given equation:

Seela rented raft from River Rafter’s inc

Cost of initial rent for raft = $\$100$

Costof rent per hour = $\$25$

Martin rented a raft from Oscar’s Outdoor shop.

Cost of initial rent for raft = $\$50$

Cost of rent per hour = $\$35$

Let $\text{'}C\text{'}$ be the total cost.

Let $\text{'}x\text{'}$ be number of hours.

Seela rented raft from River Rafter’s inc

Cost of initial rent for raft = $\$100$

Cost of rent per hour = $\$25$

1 hour $\to \$25$

Multiplying with $x$ on both sides

We get

  $\begin{array}{l}\Rightarrow 1\times x\to 25\times x\\ \Rightarrow x\to 25x\end{array}$

Therefore, Cost for $x$ hours = $\$25x$

Total cost for Seela is

  $C=$ initial cost + Cost for $\text{'}x\text{'}$ hours

  $\Rightarrow C=100+25x$

Martin rented a raft from Oscar’s Outdoor shop.

Cost of initial rent for raft = $\$50$

Cost of rent per hour = $\$35$

1 hour $\to \$35$

Multiplying with $x$ on both sides

We get

  $\begin{array}{l}\Rightarrow 1\times x\to 35\times x\\ \Rightarrow x\to 35x\end{array}$

Therefore, Cost for $x$ hours = $\$35x$

Total cost for Martin is

  $C=$ initial cost + Cost for $\text{'}x\text{'}$ hours

  $\Rightarrow C=50+35x$

We got

Total cost for Seela is $C=100+25x$

Total cost for Martin is $C=50+35x$

Given

We need to find number of hours at which Both total costs will be equal.

So, Equating both Total costs

We get

  $\begin{array}{l}\Rightarrow 100+25x=50+35x\\ \Rightarrow 35x-25x=100-50\\ \Rightarrow 10x=50\\ \Rightarrow x=\frac{50}{10}\\ \Rightarrow x=5\end{array}$

Therefore,

Number of hours at which both total costs will be equal is 5 hours.