1. **Problem statement:** Ryan earns $10 per hour for a 40-hour week. Overtime is paid at double-time. We need to find: (a) His earnings for 40 hours at normal rate. (b) The overtime rate. (c) The number of overtime hours worked if his gross pay was 500 last week. 2. **Formulas and rules:** - Normal pay = hourly rate \times hours worked. - Overtime pay rate = 2 \times normal hourly rate. - Total pay = normal pay + (overtime hours \times overtime rate). 3. **Part (a): Calculate normal weekly pay** $$\text{Normal pay} = 10 \times 40 = 400$$ 4. **Part (b): Calculate overtime rate** $$\text{Overtime rate} = 2 \times 10 = 20$$ 5. **Part (c): Calculate overtime hours worked** Given total pay = 500, normal pay = 400, overtime rate = 20. Set up equation: $$500 = 400 + 20 \times h$$ where $h$ is overtime hours. Subtract 400 from both sides: $$500 - 400 = 20 \times h$$ $$100 = 20 \times h$$ Divide both sides by 20: $$\frac{100}{\cancel{20}} = h = \frac{100}{\cancel{20}} = 5$$ So, Ryan worked 5 hours of overtime last week. **Final answers:** (a) 400 (b) 20 (c) 5