Renee and Leisa are saving money so they can visit their grandmother on a holiday.
Renee has $100 and plans to save $30 each week.
Leisa has $200 and plans to save $10 each week.
- Write an equation to represent
(i) Renee's savings (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
(ii) Leisa's savings (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- Complete the following tables of values for the equations above. (2 marks)
Renee's savings
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Weeks }(w) \ \rule[-1ex]{0pt}{0pt} &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ &\ \ 3\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Savings }(s) \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array}\(\ \ \ \ \ \ \ \) Leisa's savings
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex}\text{Weeks }(w) \ \rule[-1ex]{0pt}{0pt} &\ \ 0\ \ &\ \ 1\ \ &\ \ 2\ \ &\ \ 3\ \ \\
\hline
\rule{0pt}{2.5ex} \text{Savings }(s) \ \rule[-1ex]{0pt}{0pt} & & & & \\
\hline
\end{array} - Using the tables of values, graph both equations on the number plane below. Be sure to extend your lines to the end of the grid. (2 marks)
- After how many weeks will Renee and Leisa have saved the same amount? (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
a. (i) \(s=100+30w\)
(ii) \(s=200+10w\)
b.
|
\(\text{Renee’s savings: }s=100+30w\) |
\(\ \ \ \ \ \ \ \) |
\(\text{Leisa’s savings: }s=200+10w\) |
c.
d. \(5\ \text{weeks}\)
a. (i) \(s=100+30w\)
(ii) \(s=200+10w\)
b.
|
\(\text{Renee’s savings: }s=100+30w\) |
\(\ \ \ \ \ \ \ \) |
\(\text{Leisa’s savings: }s=200+10w\) |
c.
d. \(\text{Method 1 – Graphically by inspection}\)
\(\text{Lines intersect when }w=5\ \text{and }s=$250\)
\(\text{Method 2 – Algebraically}\)
\(\text{Solve }s=100+30w\ \text{ and }s=200+10w\ \text{simultaneously}\)
| \(100+30w\) | \(=200+10w\) |
| \(30w-10w\) | \(=200-100\) |
| \(20w\) | \(=100\) |
| \(w\) | \(=\dfrac{100}{20}=5\) |
\(\therefore\ \text{Amounts are equal after }5 \text{ weeks}.\)