Question: 20 Australian dollars = 540 South African rands
3 (a)
South African rand
Australian dollar
(i) On the grid, draw a conversion graph between Australian dollars and South African rands.
(ii) A watch costs 1350 South African rands.
Find the cost of this watch in Australian dollars.
1. **State the problem:** We are given that 20 Australian dollars (AUD) equals 540 South African rands (ZAR). We need to:
(i) Draw a conversion graph between AUD and ZAR.
(ii) Find the cost in AUD of a watch costing 1350 ZAR.
2. **Formula and rules:** The relationship between AUD and ZAR is linear and proportional. The conversion rate $r$ is given by:
$$r = \frac{540}{20} = 27$$
This means 1 AUD = 27 ZAR.
3. **Graph (i):** The graph is a straight line through the origin $(0,0)$ and the point $(20,540)$ on the coordinate grid with x-axis as AUD and y-axis as ZAR.
4. **Find the cost in AUD (ii):** Let $x$ be the cost in AUD for 1350 ZAR.
Using the conversion rate:
$$27 = \frac{540}{20} = \frac{1350}{x}$$
Cross-multiply:
$$27x = 1350$$
Divide both sides by 27:
$$x = \frac{1350}{27}$$
Show cancellation:
$$x = \frac{\cancel{1350}^{50 \times 27}}{\cancel{27}} = 50$$
5. **Answer:** The watch costs **50 Australian dollars**.