Julie cleans carpets and upholstery. She charges a $40 call-out fee and $20 for every hour it takes to complete a job.
- Complete the table of values below, where \(\large h\) represents the number of hours Julie works and \(\large w\) represents her total wage. (2 marks)
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Hours }(h) \ \rule[-1ex]{0pt}{0pt} &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ &\ \ 3\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Wage }(w) \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array} - Write an equation to represent Julie's wages, using the variables \(h\) and \(w\). (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- Graph the equation of the line representing Julie'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 Julie have to clean to earn $150? (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\ \ &\ \ 1\ \ &\ \ 2\ \ &\ \ 3\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Wage }(w) \ \rule[-1ex]{0pt}{0pt} & 40 & 60 & 80 & 100 \\
\hline
\end{array}
b. \(w=40+20h\)
c.
d. \(5.5\ \text{hours}\)
a. \(\text{Table of values}\)
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Hours }(h) \ \rule[-1ex]{0pt}{0pt} &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ &\ \ 3\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Wage }(w) \ \rule[-1ex]{0pt}{0pt} & 40 & 60 & 80 & 100 \\
\hline
\end{array}
b. \(w=40+20h\)
c.
d. \(\text{Method 1 – Graphically by inspection}\)
\(\text{When }w=150 , h=5.5\ \text{hours}\)
\(\text{Method 2 – Algebraically}\)
| \(w\) | \(=40+20h\) | |
| \(150\) | \(=40+20h\) | |
| \(20h\) | \(=150-40\) | |
| \(20h\) | \(=110\) | |
| \(h\) | \(=\dfrac{110}{20}=5.5\) |
\(\therefore\ \text{Julie would have to work for }5.5\text{ hours to earn } $150.\)