Answer :
Certainly! Let's break down the problem step by step to find out how many hours Ruth hired the plumber for.
Problem Analysis:
- Hourly rate (excluding tax): £40
- Sales tax rate: 15% or 0.15
- Total bill: £368
Step-by-Step Solution:
1. Calculate the effective hourly rate including the sales tax:
The plumber's hourly rate is £40. We need to include the sales tax of 15%.
Formula to calculate the effective hourly rate:
[tex]\[ \text{Effective hourly rate} = \text{Hourly rate} \times (1 + \text{Sales tax rate}) \][/tex]
Substitute the given values:
[tex]\[ \text{Effective hourly rate} = 40 \times (1 + 0.15) = 40 \times 1.15 = 46 \][/tex]
So, the effective hourly rate, including tax, is £46 per hour.
2. Calculate the number of hours hired using the total bill:
The total bill is £368. We can find the number of hours hired by dividing the total bill by the effective hourly rate.
Formula to calculate the number of hours:
[tex]\[ \text{Number of hours} = \frac{\text{Total bill}}{\text{Effective hourly rate}} \][/tex]
Substitute the given values:
[tex]\[ \text{Number of hours} = \frac{368}{46} = 8 \][/tex]
Therefore, Ruth hired the plumber for 8 hours.
Conclusion:
Ruth hired the plumber for 8 hours.
Problem Analysis:
- Hourly rate (excluding tax): £40
- Sales tax rate: 15% or 0.15
- Total bill: £368
Step-by-Step Solution:
1. Calculate the effective hourly rate including the sales tax:
The plumber's hourly rate is £40. We need to include the sales tax of 15%.
Formula to calculate the effective hourly rate:
[tex]\[ \text{Effective hourly rate} = \text{Hourly rate} \times (1 + \text{Sales tax rate}) \][/tex]
Substitute the given values:
[tex]\[ \text{Effective hourly rate} = 40 \times (1 + 0.15) = 40 \times 1.15 = 46 \][/tex]
So, the effective hourly rate, including tax, is £46 per hour.
2. Calculate the number of hours hired using the total bill:
The total bill is £368. We can find the number of hours hired by dividing the total bill by the effective hourly rate.
Formula to calculate the number of hours:
[tex]\[ \text{Number of hours} = \frac{\text{Total bill}}{\text{Effective hourly rate}} \][/tex]
Substitute the given values:
[tex]\[ \text{Number of hours} = \frac{368}{46} = 8 \][/tex]
Therefore, Ruth hired the plumber for 8 hours.
Conclusion:
Ruth hired the plumber for 8 hours.
Answer:
Ruth hired the plumber for 8 hours.
Step-by-step explanation:
The equation for the cost is
C = (40h) * 1.15 where h is the number of hours
368 = (40h) * 1.15
Divide each side by 1.15
320 is the cost before tax
320=40h
Divide each side by 40
8=h
Ruth hired the plumber for 8 hours.
