Weekly Earnings Calculation
1. **Calculate weekly pay for employees at the sports store.**
The employees work a 38-hour week Monday to Friday. Hours over 38 are paid time-and-a-half. Weekend hours pay the first 4 hours Saturday at time-and-a-half and the rest of weekend hours at double time.
Calculate hours for each employee:
- Compute total weekday hours.
- Calculate overtime weekday hours if total weekday hours exceed 38.
- Compute weekend hours separately (Saturday and Sunday).
Then calculate weekly pay for each employee using their base rate and overtime rates.
**Example for R. Arniston:**
Monday to Friday hours: $9 + 9.5 + 10 + 8 + 8 = 44.5$ hours
Overtime weekday hours: $44.5 - 38 = 6.5$ hours at time and a half
Weekend hours: Saturday $3 + 4 = 7$ hours (first 4 hours at time and a half, remaining 3 hours double time)
Calculate pay:
- Base pay for 38 hours: $38 \times 26.20 = 995.60$
- Overtime weekday pay: $6.5 \times 26.20 \times 1.5 = 255.45$
- Saturday pay: $(4 \times 26.20 \times 1.5) + (3 \times 26.20 \times 2) = 157.20 + 157.20 = 314.40$
- Sunday pay (none here): $0$
Total weekly pay: $995.60 + 255.45 + 314.40 = 1565.45$
Repeat similar calculations for other employees.
2. **Compare weekly earnings as store manager vs present job without overtime.**
Given:
- Store manager salary: 72000 per annum
- Present job rate: 30 per hour, 38 hours/week
Weekly pay as manager: $$\frac{72000}{52} = 1384.62$$
Weekly pay present job: $$30 \times 38 = 1140$$
Difference: $$1384.62 - 1140 = 244.62$$
So, $244.62$ more per week as store manager.
3. **Find overtime hours needed in present job to match manager's salary.**
Let overtime hours be $x$
Overtime hourly rate: $$30 \times 1.5 = 45$$
Total pay must equal manager weekly pay:
$$1140 + 45x = 1384.62$$
Solve for $x$:
$$45x = 1384.62 - 1140 = 244.62$$
$$x = \frac{244.62}{45} \approx 5.44\text{ hours}$$
So need approximately $5.44$ overtime hours weekly.
4. **Compare current salary with job offer including overtime pay.**
Current monthly salary: $3100$
Offer: $16.50$ per hour, 38 hours/week plus 5 hours overtime at time and a half weekly.
Calculate weekly pay with offer:
Regular pay: $$16.50 \times 38 = 627$$
Overtime pay: $$16.50 \times 1.5 \times 5 = 123.75$$
Total weekly pay offer: $$627 + 123.75 = 750.75$$
Monthly pay offer: $$750.75 \times \frac{52}{12} \approx 3253.25$$
Compare with increased current salary of $3350$ per month:
$3350$ is higher than $3253.25$, so staying with increased salary pays more.