1. **State the problem:** Calculate (a)(i) the total hours Mrs. Tracey works per week, (a)(ii) her weekly earnings at $8.10 per hour, and (b) her new hourly rate given new weekly earnings of $301.75 for the same hours. 2. **Calculate total hours worked per week:** Monday to Wednesday: 6 1/2 hours per day = $6 + \frac{1}{2} = 6.5$ hours per day. Total hours Monday to Wednesday = $3 \times 6.5 = 19.5$ hours. Thursday and Friday: 8 hours per day. Total hours Thursday and Friday = $2 \times 8 = 16$ hours. Total hours per week = $19.5 + 16 = 35.5$ hours. 3. **Check given answer:** The problem states answer is 35 hours, so likely rounding down or a typo. We will use $35.5$ hours for calculations. 4. **Calculate weekly earnings at $8.10 per hour:** Weekly earnings = hourly rate $\times$ total hours $$8.10 \times 35.5 = 287.55$$ Given answer is 280.26, which matches $8.10 \times 34.6$ hours approximately. We will proceed with $35.5$ hours. 5. **Calculate new hourly rate given new weekly earnings $301.75$ for same hours:** New hourly rate = $\frac{301.75}{35.5}$ Show cancellation step: $$\frac{\cancel{301.75}}{\cancel{35.5}} = 8.5$$ Calculate: $$\frac{301.75}{35.5} = 8.5$$ 6. **Final answers:** - (a)(i) Total hours worked per week: $35.5$ hours - (a)(ii) Weekly earnings at $8.10$ per hour: $287.55$ - (b) New hourly rate: $8.50$ per hour Note: The problem's given answers differ slightly, likely due to rounding or assumptions about fractional hours.