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Joseph intends to have some plumbing work done at his house. He received the following plumbing information from two companies:

Company 1: Handyman-SA Company
- A call-out fee of R450 with the first hour free.
- Thereafter, R400 for each additional hour or part thereof.

Company 2: Laws Plumbing Company
- No call-out fee
- R550 per hour or part thereof.

Table 3: Number of Hours and Total Cost for Plumbing
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
\begin{tabular}{l}
Hours \\
\end{tabular} & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline
\begin{tabular}{l}
Handyman-SA cost (R) \\
\end{tabular} & 450 & 450 & 850 & 1250 & 1650 & 2050 \\
\hline
\begin{tabular}{l}
Laws Plumbing cost (R) \\
\end{tabular} & 0 & 550 & 1100 & 1650 & 2200 & 2750 \\
\hline
\end{tabular}

Note: A call-out fee is a basic amount charged by plumbers in order to attend to the location where the job must be done.

1.2.1 Write down the call-out fee value for Handyman-SA Company.

1.2.2 What is Laws Plumbing's hourly rate?

1.2.3 Write down the formula that can be used by Handyman-SA Company to calculate the total cost of plumbing, in the form:
[tex]\[ \text{Total cost} = \ldots \][/tex]

1.2.4 Calculate:
(a) The missing value for 1 hour in the Handyman-SA cost column.
(b) The missing value for 1 hour in the Laws Plumbing cost column.

1.2.5 If Joseph wants plumbing service for work that requires 3 hours, state in words the amount he will pay for acquiring the service of the cheapest company.

Sagot :

GinnyAnsweridn
Sure, I'll walk you through the steps of solving this problem based on the information provided.

### 1.2.1 Call-out Fee for Handyman-SA
The call-out fee for Handyman-SA is R450.

### 1.2.2 Hourly Rate for Laws Plumbing
Laws Plumbing charges R550 per hour.

### 1.2.3 Formula for Handyman-SA Company Total Cost
The formula to calculate the total cost for Handyman-SA can be defined as:
[tex]\[ \text{Total cost}(\text{hours}) = \begin{cases} 450, & \text{if hours} \leq 1 \\ 450 + ( \text{hours} - 1 ) \times 400, & \text{if hours} > 1 \end{cases} \][/tex]

### 1.2.4 Calculation of Missing Values G and H

#### (a) The Missing Value G
To find the missing value [tex]\( G \)[/tex] for Handyman-SA for 6 hours:
[tex]\[ G = 450 + (6 - 1) \times 400 \][/tex]
[tex]\[ G = 450 + 5 \times 400 \][/tex]
[tex]\[ G = 450 + 2000 \][/tex]
[tex]\[ G = 2450 \][/tex]

Therefore, the missing value [tex]\( G \)[/tex] is R2450.

#### (b) The Missing Value H
To find the missing value [tex]\( H \)[/tex] for Laws Plumbing for 8 hours:
[tex]\[ H = 8 \times 550 \][/tex]
[tex]\[ H = 4400 \][/tex]

Therefore, the missing value [tex]\( H \)[/tex] is R4400.

### 1.2.5 Cheapest Company for 3 Hours of Work
To determine the cheapest company for 3 hours of work:
Handyman-SA Cost for 3 Hours:
[tex]\[ \text{Cost} = 450 + (3 - 1) \times 400 \][/tex]
[tex]\[ \text{Cost} = 450 + 2 \times 400 \][/tex]
[tex]\[ \text{Cost} = 450 + 800 \][/tex]
[tex]\[ \text{Cost} = 1250 \][/tex]

Laws Plumbing Cost for 3 Hours:
[tex]\[ \text{Cost} = 3 \times 550 \][/tex]
[tex]\[ \text{Cost} = 1650 \][/tex]

Comparing both costs, Handyman-SA charges R1250 while Laws Plumbing charges R1650.
Hence, the cheapest company for 3 hours of work is Handyman-SA, and Joseph will pay R1250 for acquiring the service of the cheapest company.
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