1. (b) (i) Problem: Calculate Ria's earnings for 40 hours at a rate of 13.50 per hour. Calculation: $$ 40 \times 13.50 = 540 $$ Answer: Ria earned 540 that week. 2. (b) (ii) Problem: Show Ria worked 15 hours overtime in August given gross earnings of 2463.75, regular hours 40 per week, 4 weeks, and overtime rate 1.5 times hourly rate. Step 1: Calculate regular earnings for 4 weeks at 40 hours/week: $$ 4 \times 40 \times 13.50 = 2160 $$ Step 2: Calculate overtime earnings: $$ 2463.75 - 2160 = 303.75 $$ Step 3: Calculate overtime hourly rate: $$ 13.50 \times 1.5 = 20.25 $$ Step 4: Calculate overtime hours: $$ \frac{303.75}{20.25} = 15 $$ Answer: Ria worked 15 hours overtime. 3. (b) (iii) Problem: Calculate Ria's remaining money after 20% tax on gross earnings 2463.75. Calculation: Tax deduction: $$ 0.20 \times 2463.75 = 492.75 $$ Remaining money: $$ 2463.75 - 492.75 = 1971 $$ Answer: Ria has 1971 left after tax. 4. (b) (iv) Problem: Calculate simple interest on 219 invested for 3 years at 4.5% per annum. Formula: $$ I = P \times r \times t $$ Substitute: $$ I = 219 \times 0.045 \times 3 = 29.565 $$ Answer: Interest received after 3 years is 29.565. 5. (c) Thomas invested 1498 at 6% simple interest per annum. (i) Calculate interest after 6 months (0.5 years): $$ I = 1498 \times 0.06 \times 0.5 = 44.94 $$ (ii) Total amount after 3 years: $$ A = P + I = 1498 + (1498 \times 0.06 \times 3) = 1498 + 269.64 = 1767.64 $$ (iii) Calculate time to earn 449.40 interest: $$ 449.40 = 1498 \times 0.06 \times t \Rightarrow t = \frac{449.40}{1498 \times 0.06} = 5 \text{ years} $$ 6. (c) Mr Adams invested 5000 and received 5810 after 3 years. (i) Simple interest earned: $$ I = 5810 - 5000 = 810 $$ (ii) Annual interest rate: $$ 810 = 5000 \times r \times 3 \Rightarrow r = \frac{810}{5000 \times 3} = 0.054 = 5.4\% $$ (iii) Time to double investment: $$ 2 \times 5000 = 5000 + 5000 \times 0.054 \times t \Rightarrow 10000 = 5000 + 270 t $$ $$ 5000 = 270 t \Rightarrow t = \frac{5000}{270} \approx 18.52 \text{ years} $$