1. **Problem 10a:** Jim receives holiday loading of 17.5% of 4 weeks pay, and the loading amount is 996.80. We need to find his normal weekly pay.
2. The formula for holiday loading is:
$$\text{Holiday Loading} = 0.175 \times 4 \times \text{Weekly Pay}$$
3. Substitute the known values:
$$996.80 = 0.175 \times 4 \times \text{Weekly Pay}$$
4. Simplify the right side:
$$996.80 = 0.7 \times \text{Weekly Pay}$$
5. To find Weekly Pay, divide both sides by 0.7:
$$\text{Weekly Pay} = \frac{996.80}{0.7}$$
6. Show cancellation:
$$\text{Weekly Pay} = \frac{\cancel{996.80}}{\cancel{0.7}} = 1424$$
7. So, Jim's normal weekly pay is $1424.
8. **Problem 10b:** Find Jim's normal hourly pay rate if he works 40 hours a week.
9. Hourly pay rate formula:
$$\text{Hourly Pay} = \frac{\text{Weekly Pay}}{\text{Hours per week}}$$
10. Substitute values:
$$\text{Hourly Pay} = \frac{1424}{40}$$
11. Simplify:
$$\text{Hourly Pay} = 35.6$$
12. Jim's normal hourly pay rate is $35.60.
13. **Problem 11a:** Chloe’s annual salary is 72800. Calculate her weekly wage.
14. There are 52 weeks in a year, so:
$$\text{Weekly Wage} = \frac{72800}{52}$$
15. Simplify:
$$\text{Weekly Wage} = 1400$$
16. Chloe’s weekly wage is $1400.
17. **Problem 11b:** Holiday loading is 17.5% of four weeks pay. Calculate Chloe’s holiday loading.
18. Calculate 4 weeks pay:
$$4 \times 1400 = 5600$$
19. Calculate holiday loading:
$$0.175 \times 5600 = 980$$
20. Chloe’s holiday loading is $980.
21. **Problem 11c:** Chloe’s employer increases her annual salary by 1%. Calculate new salary.
22. Increase amount:
$$0.01 \times 72800 = 728$$
23. New annual salary:
$$72800 + 728 = 73528$$
24. Chloe’s new annual salary is $73528.
25. **Problem 11d:** Explain why Chloe is worse off financially with the 1% increase.
26. Chloe loses holiday loading of $980 but gains only $728 from the 1% increase.
27. Since $728 < $980, she is worse off by $252.
28. So, the increase does not fully compensate for the lost holiday loading.
Pay Calculations 43C790
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.