Jeremy owns a paddle board hire company. He charges a $20 insurance fee with every hire and $35 for every hour of hire.
- Complete the table of values below, where \(\large h\) represents the number of hours of hire and \(\large w\) represents his total earnings for each hour of hire. (2 marks)
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Hours }(h) \ \rule[-1ex]{0pt}{0pt} &\ \ 0\ \ &\ \ 2\ \ &\ \ 4\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Wage }(w) \ \rule[-1ex]{0pt}{0pt} & & & \\
\hline
\end{array} - Write an equation to represent Jeremy's wages, using the variables \(h\) and \(w\). (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- Graph the equation of the line representing Jeremy's wages on the number plane below. Be sure to extend your line to the edge of the grid. (2 marks)
- For how many hours would Jeremy have to hire a paddle board to earn $230? (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
a.
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Hours }(h) \ \rule[-1ex]{0pt}{0pt} &\ \ 0\ \ &\ \ 2\ \ &\ \ 4\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Wage }(w) \ \rule[-1ex]{0pt}{0pt} & 20 & 90 & 160 \\
\hline
\end{array}
b. \(w=20+35h\)
c.
d. \(6\ \text{hours}\)
a. \(\text{Table of values}\)
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Hours }(h) \ \rule[-1ex]{0pt}{0pt} &\ \ 0\ \ &\ \ 2\ \ &\ \ 4\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Wage }(w) \ \rule[-1ex]{0pt}{0pt} & 40 & 90 & 160 \\
\hline
\end{array}
b. \(w=20+35h\)
c.
d. \(\text{Method 1 – Graphically by inspection}\)
\(\text{When }w=230 , h=6\ \text{hours}\)
\(\text{Method 2 – Algebraically}\)
| \(w\) | \(=20+35h\) | |
| \(230\) | \(=20+35h\) | |
| \(35h\) | \(=230-20\) | |
| \(35h\) | \(=210\) | |
| \(h\) | \(=\dfrac{210}{35}=6\) |
\(\therefore\ \text{Jeremy would have to hire a board for }6\text{ hours to earn } $230.\)