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QUESTION 3: [12 MARKS]

Lebo is a learner who lives in the Stanger area. He attends Stanger Comprehensive School, which has an enrolment of 450 learners. The school had many fund-raising activities during the course of the year. They raised an amount of R24,500 towards the school sports and fun day. Meals were budgeted at R18 per learner. Sound and entertainment amounted to [tex]$10 \%$[/tex] of the total amount raised. Mr. Pillay, the school principal, decided to donate R8,000. The sports stadium costs double the amount spent on banners and tags.

3.1. Study the budget for the school sports and fun day, then answer the questions set:

\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{INCOME} & \multicolumn{2}{c|}{EXPENSES} \\
\hline Income from fund raising & R24,500 & Hire of stadium & A \\
\hline Donation & R8,000 & Meals & B \\
\hline & & Banners \& tags & R1,250 \\
\hline & & Sound and entertainment & C \\
\hline & & Admin \& telephone & R250 \\
\hline TOTAL INCOME & D & & \\
\hline AMOUNT LEFT OVER AFTER EXPENSES HAVE BEEN PAID & E \\
\hline
\end{tabular}

3.1.1. Calculate the values indicated by [tex]$A, B, C, D,$[/tex] and [tex]$E$[/tex]. [tex]$(10)$[/tex]

3.1.2. Verify whether a surplus or a deficit was made. Substantiate your answer. [tex]$(2)$[/tex]

Sagot :

GinnyAnsweridn
Alright, let's break down the problem and solve it step-by-step.

### Step-by-Step Solution:

Given data:

- Fund raised amount: [tex]\( R24,500 \)[/tex]
- Donation amount: [tex]\( R8,000 \)[/tex]
- Number of learners: [tex]\( 450 \)[/tex]
- Meal cost per learner: [tex]\( R18 \)[/tex]
- Cost for banners and tags: [tex]\( R1,250 \)[/tex]
- Admin and telephone costs: [tex]\( R250 \)[/tex]
- Sound and entertainment: [tex]\( 10\% \)[/tex] of the fund raised amount

Step 1: Calculate total income (D)

Total income, [tex]\( D \)[/tex], is calculated by adding the fund-raised amount and the donation:
[tex]\[ D = 24,500 + 8,000 = R32,500 \][/tex]

Step 2: Calculate sound and entertainment cost (C)

Sound and entertainment cost, [tex]\( C \)[/tex], is [tex]\( 10\% \)[/tex] of the fund raised amount:
[tex]\[ C = 0.10 \times 24,500 = R2,450 \][/tex]

Step 3: Calculate cost of meals (B)

Total meal cost, [tex]\( B \)[/tex], is calculated by multiplying the number of learners by the cost per learner:
[tex]\[ B = 450 \times 18 = R8,100 \][/tex]

Step 4: Calculate the cost of hiring the stadium (A)

The stadium cost, [tex]\( A \)[/tex], is double the cost of banners and tags:
[tex]\[ A = 2 \times 1250 = R2,500 \][/tex]

Step 5: Calculate total expenses

Total expenses are the sum of stadium cost, meal cost, banners and tags cost, sound and entertainment cost, and admin and telephone cost:
[tex]\[ \text{Total expenses} = A + B + 1250 + C + 250 \][/tex]
[tex]\[ \text{Total expenses} = 2500 + 8100 + 1250 + 2450 + 250 = R14,550 \][/tex]

Step 6: Calculate the amount left over after expenses (E)

The amount left over, [tex]\( E \)[/tex], is calculated by subtracting the total expenses from the total income:
[tex]\[ E = D - \text{Total expenses} \][/tex]
[tex]\[ E = 32,500 - 14,550 = R17,950 \][/tex]

### Summary of Calculations:

- [tex]\( A = R2,500 \)[/tex]
- [tex]\( B = R8,100 \)[/tex]
- [tex]\( C = R2,450 \)[/tex]
- [tex]\( D = R32,500 \)[/tex]
- [tex]\( E = R17,950 \)[/tex]

### Verification: Surplus or Deficit

If the amount left over (E) is positive, a surplus was made. If it is negative, a deficit was made.

Here,
[tex]\[ E = R17,950 > 0 \][/tex]

Thus, a surplus of R17,950 was made.

### Final Answer:

3.1.1. Calculated Values:
- [tex]\( A = R2,500 \)[/tex]
- [tex]\( B = R8,100 \)[/tex]
- [tex]\( C = R2,450 \)[/tex]
- [tex]\( D = R32,500 \)[/tex]
- [tex]\( E = R17,950 \)[/tex]

3.1.2. Verification:
A surplus of R17,950 was made, as the amount left over is positive.
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