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QUESTION 2

Masakhane community rents out a hall at a cost of R750 per event hosted. The local municipality provides the community with a fixed monthly income of R500 to assist in maintaining its facilities. The monthly fixed expenses to maintain the hall facilities are R3000, with an additional expense of R250 per event hosted.

Table 1 below shows the total monthly income and the total monthly expenses for the hall when renting out the hall.

TABLE 1: INCOME AND EXPENSES FOR RENTING OUT A HALL
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline \begin{tabular}{l}
Number of events \\
hosted in a month
\end{tabular} & 0 & 1 & 2 & 3 & 5 & 10 \\
\hline \begin{tabular}{l}
Income in Rands \\
(R)
\end{tabular} & A & 1250 & 2000 & 2750 & B & 8000 \\
\begin{tabular}{l}
Total monthly \\
expense in Rands \\
(R)
\end{tabular} & 3000 & 3250 & 3500 & C & 4250 & 5500 \\
\hline
\end{tabular}

Use the information above to answer the questions that follow.

2.1 Determine the formula that can be used to calculate the total monthly expenses.
2.2 Calculate the missing values: [tex]$A, B,$[/tex] and [tex]$C$[/tex].
2.3 Use the ANSWER SHEET provided to draw the graph of monthly income and monthly expenses on the same set of axes.
2.4 Explain the term break-even point in the given context.
2.5 Determine the number of events in a month that Masakhane community must host to break even.

(17)



Answer :

GinnyAnswer
Sure, let's break down and solve the questions step by step.

### 2.1 Determine the formula that can be used to calculate the total monthly expenses.

To determine the monthly expenses for renting out the hall, we need to take into account both fixed expenses and variable expenses:

1. Fixed monthly expenses = R 3000
2. Variable expense per event = R 250

So, if [tex]\( x \)[/tex] is the number of events hosted in a month:
[tex]\[ \text{Total Monthly Expenses} = \text{Fixed Expenses} + (\text{Variable Expense per Event} \times \text{Number of Events}) \][/tex]
[tex]\[ \text{Total Monthly Expenses} = 3000 + (250 \times x) \][/tex]

### 2.2 Calculate the missing values: A, B, and C.

Now, we will calculate the missing values [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex]:

- A: Income when no events are hosted ([tex]\( x = 0 \)[/tex]).
- B: Income when 5 events are hosted ([tex]\( x = 5 \)[/tex]).
- C: Expenses when 3 events are hosted ([tex]\( x = 3 \)[/tex]).

Income Calculation:
[tex]\[ \text{Total Monthly Income} = \text{Fixed Income} + (\text{Rent per Event} \times \text{Number of Events}) \][/tex]
The fixed monthly income is R 500 and the rent per event is R 750.

1. For [tex]\( A \)[/tex]: When no events are hosted ([tex]\( x = 0 \)[/tex]):
[tex]\[ \text{Income} = 500 + (750 \times 0) = 500 \][/tex]
So, [tex]\( A = 500 \)[/tex]

2. For [tex]\( B \)[/tex]: When 5 events are hosted [tex]\(( x = 5 \)[/tex]):
[tex]\[ \text{Income} = 500 + (750 \times 5) = 500 + 3750 = 4250 \][/tex]
So, [tex]\( B = 4250 \)[/tex]

Expense Calculation:
[tex]\[ \text{Total Monthly Expenses} = 3000 + (250 \times \text{Number of Events}) \][/tex]

1. For [tex]\( C \)[/tex]: When 3 events are hosted ([tex]\( x = 3 \)[/tex]):
[tex]\[ \text{Total Monthly Expenses} = 3000 + (250 \times 3) = 3000 + 750 = 3750 \][/tex]
So, [tex]\( C = 3750 \)[/tex]

### 2.3 Use the ANSWER SHEET provided to draw the graph of monthly income and monthly expenses on the same set of axes.

(Since I cannot draw graphs, please use the following data points to plot the graph.)

For plotting the graph:

Income Data Points (based on [tex]\( x \)[/tex]):
- [tex]\( x = 0 \)[/tex]: Income = 500
- [tex]\( x = 1 \)[/tex]: Income = 1250
- [tex]\( x = 2 \)[/tex]: Income = 2000
- [tex]\( x = 3 \)[/tex]: Income = 2750
- [tex]\( x = 5 \)[/tex]: Income = 4250
- [tex]\( x = 10 \)[/tex]: Income = 8000

Expenses Data Points (based on [tex]\( x \)[/tex]):
- [tex]\( x = 0 \)[/tex]: Expense = 3000
- [tex]\( x = 1 \)[/tex]: Expense = 3250
- [tex]\( x = 2 \)[/tex]: Expense = 3500
- [tex]\( x = 3 \)[/tex]: Expense = 3750
- [tex]\( x = 5 \)[/tex]: Expense = 4250
- [tex]\( x = 10 \)[/tex]: Expense = 5500

### 2.4 Explain the term break-even point in the given context.

The break-even point in this context is the number of events hosted in a month where the total monthly income equals the total monthly expenses. At this point, the community neither makes a profit nor incurs a loss; income covers all the expenses.

### 2.5 Determine the number of events in a month that Masakhane community must host to break even.

To find the break-even point, we set the monthly income equal to the monthly expenses and solve for the number of events:

Income:
[tex]\[ \text{Income} = 500 + 750x \][/tex]

Expenses:
[tex]\[ \text{Expense} = 3000 + 250x \][/tex]

Set the two equations equal to each other:
[tex]\[ 500 + 750x = 3000 + 250x \][/tex]

Rearrange to solve for [tex]\( x \)[/tex]:
[tex]\[ 750x - 250x = 3000 - 500 \][/tex]
[tex]\[ 500x = 2500 \][/tex]
[tex]\[ x = \frac{2500}{500} \][/tex]
[tex]\[ x = 5 \][/tex]

So, the number of events in a month that the Masakhane community must host to break even is 5.

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