Grade 12 learners from Mollo High School are selling apples during lunch break to raise funds for their…

Question

Grade 12 learners from Mollo High School are selling apples during lunch break to raise funds for their matric farewell function. They have asked the Principal to use the school tuck-shop. They bought a crate with 116 apples for R255.00 and sold them at R3.00 each.

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Here's the breakdown for Question 2:

Question 2.1

The break-even point is the point at which total costs and total revenue are equal, meaning there is no net loss or gain. In other words, it's the point where a business has covered all its expenses but has not yet made a profit.

Question 2.2

Calculate total revenue
The selling price per apple is R3.00. They sold 116 apples.
$\text{Total Revenue} = \text{Number of apples sold} \times \text{Selling price per apple}$ $\text{Total Revenue} = 116 \times \text{R}3.00 = \text{R}348.00$
Calculate profit
The cost of the crate of 116 apples is R255.00.
$\text{Profit} = \text{Total Revenue} - \text{Cost of crate}$ $\text{Profit} = \text{R}348.00 - \text{R}255.00$ $\text{Profit} = \boxed{\text{R}93.00}$
Question 2.3.1
Calculate profit per apple
The cost per apple from the crate is $\frac{\text{R}255.00}{116}$ .
$\text{Profit per apple} = \text{Selling price per apple} - \text{Cost per apple}$ $\text{Profit per apple} = \text{R}3.00 - \frac{\text{R}255.00}{116}$ $\text{Profit per apple} = \text{R}3.00 - \text{R}2.19827...$ $\text{Profit per apple} \approx \text{R}0.80172...$
Calculate apples sold for R120 profit
Let $x$ be the number of apples sold.
$\text{Total Profit} = \text{Profit per apple} \times x$ $\text{R}120 = \left(\text{R}3.00 - \frac{\text{R}255.00}{116}\right) \times x$ $\text{R}120 = \left(\frac{3 \times 116 - 255}{116}\right) \times x$ $\text{R}120 = \left(\frac{348 - 255}{116}\right) \times x$ $\text{R}120 = \frac{93}{116} \times x$ $x = \frac{120 \times 116}{93}$ $x = \frac{13920}{93}$ $x = \boxed{150 \text{ apples}}$
Question 2.3.2
Determine the break-even point
To break even, the total revenue must equal the total cost of the crate.
$\text{Total Revenue} = \text{Cost of crate}$ $\text{Selling price per apple} \times \text{Number of apples} = \text{R}255.00$ $\text{R}3.00 \times \text{Number of apples} = \text{R}255.00$
Calculate the number of apples to break even
$\text{Number of apples} = \frac{\text{R}255.00}{\text{R}3.00}$ $\text{Number of apples} = \boxed{85 \text{ apples}}$
Question 2.3.3
Identify total amount needed and daily profit
The total amount to raise is R13 500.00.
The profit per day is R120 (from the premise of Question 2.3).
Calculate the number of days
$\text{Number of days} = \frac{\text{Total amount to raise}}{\text{Profit per day}}$ $\text{Number of days} = \frac{\text{R}13\,500.00}{\text{R}120.00/\text{day}}$ $\text{Number of days} = \boxed{112.5 \text{ days}}$
Question 2.4
Calculate value for A (Cost for Avis Car Hire for 20 km)
Avis Car Hire costs R6.50 per kilometer.
$A = 20 \text{ km} \times \text{R}6.50/\text{km}$ $A = \boxed{\text{R}130}$
Calculate value for B (Cost for Budget Car Hire for 40 km)
Budget Car Hire costs R165 plus R3.50 per kilometer.
$B = \text{R}165 + (40 \text{ km} \times \text{R}3.50/\text{km})$ $B = \text{R}165 + \text{R}140$ $B = \boxed{\text{R}305}$
Calculate value for C (Kilometres travelled for given costs)
For Avis Car Hire, the cost is R455.
$C = \frac{\text{R}455}{\text{R}6.50/\text{km}}$ $C = 70 \text{ km}$
For Budget Car Hire, the cost is R410.
$\text{R}410 = \text{R}165 + (C \times \text{R}3.50/\text{km})$ $\text{R}410 - \text{R}165 = C \times \text{R}3.50/\text{km}$ $\text{R}245 = C \times \text{R}3.50/\text{km}$ $C = \frac{\text{R}245}{\text{R}3.50/\text{km}}$ $C = \boxed{70 \text{ km}}$
The completed table is:
$\begin{array}{|l|c|c|c|c|} \hline \text{Kilometres travelled} & 10 & 20 & 40 & \textbf{70} \\ \hline \text{Cost for Avis Car Hire} & \text{R}65 & \textbf{R}130 & \text{R}260 & \text{R}455 \\ \hline \text{Cost for Budget Car Hire} & \text{R}200 & \text{R}235 & \textbf{R}305 & \text{R}410 \\ \hline \end{array}$

Grade 12 learners from Mollo High School are selling apples during lunch break to raise funds for their matric farewell function. They have asked the Principal to use the school tuck-shop. They bought a crate with 116 apples for R255.00 and sold them at R3.00 each.

Step-by-step solution

Question 2.1

Question 2.2

Calculate total revenue

Calculate profit

Question 2.3.1

Calculate profit per apple

Calculate apples sold for R120 profit

Question 2.3.2

Determine the break-even point

Calculate the number of apples to break even

Question 2.3.3

Identify total amount needed and daily profit

Calculate the number of days

Question 2.4

Calculate value for A (Cost for Avis Car Hire for 20 km)

Calculate value for B (Cost for Budget Car Hire for 40 km)

Calculate value for C (Kilometres travelled for given costs)

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