Certainly! Let's navigate through each part of the problem step by step.
### 1.1. Write down the basic fee for Protea Hotel.
The basic fee for hiring a conference room at Protea Hotel is R3600.
### 1.2. Determine the value of A.
To find the total cost of hiring the conference room when 90 tickets are sold at Bon Hotel:
[tex]\[
\text{Total cost} = \text{Number of tickets sold} \times \text{Cost per person} = 90 \times 90 = 8100 \, \text{R}
\][/tex]
So, the value of A is R8100.
### 1.3. Write down the formula that can be used to calculate the total cost of hiring the conference room at Protea Hotel.
The total cost at Protea Hotel can be written as:
[tex]\[
\text{Total cost} (R) = \text{Basic fee} + (\text{Cost per person} \times \text{Number of tickets sold})
\][/tex]
Given that the basic fee is R3600 and the cost per person is R50, the formula becomes:
[tex]\[
\text{Total cost} (R) = 3600 + 50 \times \text{Number of tickets sold}
\][/tex]
### 1.4. Hence calculate:
#### (a) B, the total cost at Protea Hotel for the given number of tickets sold.
Here, 25 tickets were sold at Protea Hotel. Plugging the values into our formula, we get:
[tex]\[
\text{Total cost} = 3600 + 50 \times 25 = 3600 + 1250 = 4850 \, \text{R}
\][/tex]
So, B is R4850.
#### (b) C, number of tickets sold.
To find the number of tickets sold (C) for a total cost of R8350:
[tex]\[
\text{Total cost} = 3600 + 50 \times \text{Number of tickets sold}
\][/tex]
Setting the total cost to R8350:
[tex]\[
8350 = 3600 + 50 \times \text{Number of tickets sold}
\][/tex]
Subtract the basic fee from both sides:
[tex]\[
4750 = 50 \times \text{Number of tickets sold}
\][/tex]
Now divide both sides by 50:
[tex]\[
\text{Number of tickets sold} = \frac{4750}{50} = 95
\][/tex]
So, C is 95 tickets.
### 1.5. If Mangaung Junior Council managed to sell only 50 tickets, which conference room would be more cost-effective to hire?
To compare costs for 50 tickets sold:
- Bon Hotel:
[tex]\[
\text{Total cost} = 50 \times 90 = 4500 \, \text{R}
\][/tex]
- Protea Hotel:
[tex]\[
\text{Total cost} = 3600 + 50 \times 50 = 3600 + 2500 = 6100 \, \text{R}
\][/tex]
Comparing the two totals, the cost at Bon Hotel is R4500 while at Protea Hotel it is R6100. Therefore, Bon Hotel would be more cost-effective to hire.
### Summary of the Answers:
1. Basic fee for Protea Hotel: R3600
2. Value of A: R8100
3. Total cost formula for Protea Hotel: [tex]\( \text{Total cost} (R) = 3600 + 50 \times \text{Number of tickets sold} \)[/tex]
4. Value of B: R4850
5. Number of tickets sold for a cost of R8350 (C): 95 tickets
6. More cost-effective hotel for 50 tickets: Bon Hotel
