To calculate the total pay for the mechanic who worked last week, we can break down the problem into several steps:
### Step 1: Identify the given data
- Normal pay rate: £10.80 per hour
- Working hours each day: [tex]\( \frac{71}{2} \)[/tex] hours
- Days worked: Monday to Saturday (6 days total), with Monday to Friday being regular days and Saturday being at an extra rate.
### Step 2: Calculate the hours worked
- Hours worked per normal working day (Monday to Friday) is:
[tex]\[
\text{Normal hours per day} = \frac{71}{2} = 35.5 \text{ hours}
\][/tex]
- Total normal working hours for 5 days (Monday to Friday) is:
[tex]\[
\text{Total normal hours} = 35.5 \times 5 = 177.5 \text{ hours}
\][/tex]
- Total extra working hours for 1 day (Saturday) is:
[tex]\[
\text{Total extra hours} = 35.5 \times 1 = 35.5 \text{ hours}
\][/tex]
### Step 3: Calculate the pay
- The normal pay is based on the regular hourly rate:
[tex]\[
\text{Normal pay} = 177.5 \times 10.80 = £1917.00
\][/tex]
- The pay for extra hours (Saturday) is at [tex]\( \frac{11}{4} \)[/tex] times the normal rate. First, we calculate the extra pay rate:
[tex]\[
\text{Extra pay rate} = \frac{11}{4} \times 10.80 = £29.70 \text{ per hour}
\][/tex]
- Now, calculate the pay for Saturday:
[tex]\[
\text{Extra pay} = 35.5 \times 29.70 = £1054.35
\][/tex]
### Step 4: Total pay
- Add the normal pay and the extra pay to get the total pay:
[tex]\[
\text{Total pay} = 1917.00 + 1054.35 = £2971.35
\][/tex]
So, by following these steps, we determine that the mechanic's total pay for last week is £2971.35.
