Answer :
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.
### 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.