The problem states a fixed base fare of R12 and an additional cost per kilometre. The table provides data poin

Question

The problem states a fixed base fare of R12 and an additional cost per kilometre. The table provides data points:

ScanSolve AI Tutor · Accepted Answer

Step 1: Analyze the given information and table.
The problem states a fixed base fare of R12 and an additional cost per kilometre. The table provides data points:
•   Monday: 5 km, R22
•   Tuesday: 9 km, R30
•   Wednesday: 14 km, R40

Step 2: Answer 1.1.
The pattern shows that the total cost (fare) increases as the distance travelled increases. There is a *fixed base fare* and an *additional cost per kilometre*, indicating a *linear relationship* between cost and distance. If a graph were drawn with distance on the x-axis and cost on the y-axis, it would form a *straight line*.

Step 3: Answer 1.2 by determining the additional cost per kilometre.
We can use any data point from the table and the given base fare of R12.
Using Monday's data:
Total cost = Base fare + (Additional cost per km $	imes$ Distance)
$$22 = 12 + (	ext{Additional cost per km} 	imes 5)$$
Subtract the base fare from the total cost to find the variable cost:
$$22 - 12 = 	ext{Additional cost per km} 	imes 5$$
$$10 = 	ext{Additional cost per km} 	imes 5$$
Divide by the distance to find the cost per kilometre:
$$	ext{Additional cost per km} = \frac{10}{5}$$
$$	ext{Additional cost per km} = 2 	ext{ R/km}$$
Using Tuesday's data as a check:
$$30 = 12 + (	ext{Additional cost per km} 	imes 9)$$
$$30 - 12 = 	ext{Additional cost per km} 	imes 9$$
$$18 = 	ext{Additional cost per km} 	imes 9$$
$$	ext{Additional cost per km} = \frac{18}{9}$$
$$	ext{Additional cost per km} = 2 	ext{ R/km}$$
The additional cost per kilometre is consistent.
The additional cost per kilometre is $\boxed{	ext{R2/km}}$.

Step 4: Answer 1.3 by writing the formula for taxi fare (C) for any distance travelled (d).
Based on the fixed base fare of R12 and the additional cost of R2 per kilometre:
$$C = 	ext{Base Fare} + (	ext{Cost per km} 	imes d)$$
$$C = 12 + 2d$$
The formula is $\boxed{C = 12 + 2d}$.

Step 5: Answer 1.4 by calculating the cost of travelling 43 miles.
First, convert 43 miles to kilometres using the conversion factor 1 km = 0.62 miles.
$$	ext{Distance in km} = \frac{	ext{Distance in miles}}{	ext{miles per km}}$$
$$	ext{Distance in km} = \frac{43 	ext{ miles}}{0.62 	ext{ miles/km}}$$
$$	ext{Distance in km} \approx 69.3548 	ext{ km}$$
Now, use the formula $C = 12 + 2d$ with $d = 69.3548$ km.
$$C = 12 + 2(69.3548)$$
$$C = 12 + 138.7096$$
$$C = 150.7096$$
Rounding to two decimal places for currency:
$$C \approx 150.71$$
The cost of travelling 43 miles is $\boxed{	ext{R150.71}}$.

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