Chapter 1, Problem 7MCQ

To determine

The expression to calculate cost of popcorn machine for 5 hours.

Also make a table.

Answer to Problem 7MCQ

  $\text{F}\left(5\right)=\$209.75$ .

Table showing cost for renting popcorn machine:

Time (hr)	Expression	Cost ($);F is cost of renting
$\text{6hr}$	$\text{F}\left(6\right)=\$35\left(x\right)+\$6.95\left(y\right)$	$\$251.7$
$\text{7hr}$	$\text{F}\left(7\right)=\$35\left(x\right)+\$6.95\left(y\right)$	$\$293.65$
$\text{8hr}$	$\text{F}\left(8\right)=\$35\left(x\right)+\$6.95\left(y\right)$	$\$335.6$

Explanation of Solution

Given:

Popcorn machine costs $35 plus $6.95 for one hour:

Calculation:

Equation for cost of popcorn machine per hour:

Suppose x is rent and y be tax for popcorn machine.

So, for 1hr;

Expression for renting popcorn machine:

  $\text{F}\left(1\right)=\$35\left(x\right)+\$6.95\left(y\right)$

So, the cost for 1hr is,

  $\begin{array}{l}\text{F}\left(1\right)=\$35\left(1\right)+\$6.95\left(1\right)\\ \text{F}\left(1\right)=\$35+\$6.95\\ \text{F}\left(1\right)=\$41.95\end{array}$

So, for 5hr;

  $\begin{array}{l}\text{F}\left(5\right)=\$35\left(5\right)+\$6.95\left(5\right)\\ \text{F}\left(5\right)=\$35\times 5+\$6.95\times 5\\ \text{F}\left(5\right)=\$175+\$34.75\\ \text{F}\left(5\right)=\$209.75\end{array}$

The cost for 5hr of renting popcornmachine is $\$209.75$ .

Table showing cost for renting popcorn machine:

Time (hr)	Expression	Cost ($);F is cost of renting
$\text{6hr}$	$\text{F}\left(6\right)=\$35\left(x\right)+\$6.95\left(y\right)$	$\$251.7$
$\text{7hr}$	$\text{F}\left(7\right)=\$35\left(x\right)+\$6.95\left(y\right)$	$\$293.65$
$\text{8hr}$	$\text{F}\left(8\right)=\$35\left(x\right)+\$6.95\left(y\right)$	$\$335.6$