Question 4 (16 marks) Commission, Rentals and Compound interest 4. Calculate where possible and leave your answers rounded off to two decimal places 4.1. Mr Mazibuko sells cakes at schools, He has asked Anele to sell on his behalf due to his busy schedule. He packs them in 3 chocolate muffins and charges R10 per pack and 3 scones at R7; 50 per pack. Anele receives R2 for every pack she sells. (3) 4.1.1. 20 packs of muffins and 20 packs of scones (3) 4.1.2. 72 packs of müffins and 15 scones many 4.1.3. If Anele sells only scones and earns \( R \) 55, 50 in commission, how scones did she sell? 4.2. Maribs' tool hire business has a variety of tools that customers can hire per working day. Mr Mabhiande hires the following tools for 3 days: a chain saw at R135 per day, a pick at R25 per day and 2 spades at R18 each per day. Calculate: 4.2.1. The total hiring cost for Mr Mabhande for 3 days (3) 4.2.2. The extra amount Mr Mabhande has to pay if he returns the tools one day toc (2) late. 4.3. Diego invests R18000 for 6 years at \( 15 \% \) p,a compounded annually. Find the future value, of his investment after 6 years and the interest he receives, (4)

Let's solve the problem step by step, extracting the known conditions and performing the necessary calculations. ### 4.1. Commission from Selling Cakes **4.1.1.** Calculate Anele's earnings from selling 20 packs of muffins and 20 packs of scones. - **Muffins:** - Price per pack = R10 - Packs sold = 20 - Total earnings from muffins = \( 20 \times 10 \) - **Scones:** - Price per pack = R7.50 - Packs sold = 20 - Total earnings from scones = \( 20 \times 7.50 \) - **Total Earnings:** - Total earnings = Earnings from muffins + Earnings from scones - Commission per pack = R2 - Total commission = \( 2 \times (20 + 20) \) Let's calculate these values. **4.1.2.** Calculate Anele's earnings from selling 72 packs of muffins and 15 packs of scones. - **Muffins:** - Packs sold = 72 - Total earnings from muffins = \( 72 \times 10 \) - **Scones:** - Packs sold = 15 - Total earnings from scones = \( 15 \times 7.50 \) - **Total Earnings:** - Total earnings = Earnings from muffins + Earnings from scones - Total commission = \( 2 \times (72 + 15) \) **4.1.3.** If Anele sells only scones and earns R55.50 in commission, how many scones did she sell? - Commission per pack = R2 - Total commission = R55.50 - Number of packs sold = \( \frac{55.50}{2} \) Now, let's perform these calculations. ### 4.2. Tool Hire Business **4.2.1.** Calculate the total hiring cost for Mr. Mabhande for 3 days. - **Chain Saw:** - Daily cost = R135 - Total cost for 3 days = \( 135 \times 3 \) - **Pick:** - Daily cost = R25 - Total cost for 3 days = \( 25 \times 3 \) - **Spades:** - Daily cost = R18 - Total cost for 2 spades for 3 days = \( 2 \times 18 \times 3 \) - **Total Hiring Cost:** - Total cost = Cost of chain saw + Cost of pick + Cost of spades **4.2.2.** Calculate the extra amount Mr. Mabhande has to pay if he returns the tools one day late. - Total daily cost for all tools = Total hiring cost calculated above - Extra amount for one day late = Total daily cost ### 4.3. Investment Calculation Diego invests R18000 for 6 years at 15% p.a. compounded annually. - Future Value (FV) formula: \[ FV = P(1 + r)^n \] where: - \( P = 18000 \) - \( r = 0.15 \) - \( n = 6 \) - Interest received = Future Value - Principal Now, let's perform all these calculations. Calculate the value by following steps: - step0: Calculate: \(\frac{55.5}{2}\) - step1: Convert the expressions: \(\frac{\frac{111}{2}}{2}\) - step2: Multiply by the reciprocal: \(\frac{111}{2}\times \frac{1}{2}\) - step3: Multiply the fractions: \(\frac{111}{2\times 2}\) - step4: Multiply: \(\frac{111}{4}\) Calculate or simplify the expression \( 135 * 3 + 25 * 3 + 2 * 18 * 3 \). Calculate the value by following steps: - step0: Calculate: \(135\times 3+25\times 3+2\times 18\times 3\) - step1: Multiply the numbers: \(405+25\times 3+2\times 18\times 3\) - step2: Multiply the numbers: \(405+75+2\times 18\times 3\) - step3: Multiply the terms: \(405+75+108\) - step4: Add the numbers: \(588\) Calculate or simplify the expression \( 135 + 25 + 2 * 18 \). Calculate the value by following steps: - step0: Calculate: \(135+25+2\times 18\) - step1: Multiply the numbers: \(135+25+36\) - step2: Add the numbers: \(196\) Calculate or simplify the expression \( 18000 * (1 + 0.15)^6 \). Calculate the value by following steps: - step0: Calculate: \(18000\left(1+0.15\right)^{6}\) - step1: Add the numbers: \(18000\times 1.15^{6}\) - step2: Convert the expressions: \(18000\left(\frac{23}{20}\right)^{6}\) - step3: Simplify: \(18000\times \frac{23^{6}}{20^{6}}\) - step4: Rewrite the expression: \(400\times 45\times \frac{23^{6}}{20^{6}}\) - step5: Rewrite the expression: \(20^{2}\times 45\times \frac{23^{6}}{20^{6}}\) - step6: Reduce the numbers: \(45\times \frac{23^{6}}{20^{4}}\) - step7: Rewrite the expression: \(5\times 9\times \frac{23^{6}}{20^{4}}\) - step8: Rewrite the expression: \(5\times 9\times \frac{23^{6}}{5^{4}\times 4^{4}}\) - step9: Reduce the numbers: \(9\times \frac{23^{6}}{5^{3}\times 4^{4}}\) - step10: Multiply: \(\frac{9\times 23^{6}}{32000}\) Calculate or simplify the expression \( 20 * 10 + 20 * 7.50 \). Calculate the value by following steps: - step0: Calculate: \(20\times 10+20\times 7.5\) - step1: Multiply the numbers: \(200+20\times 7.5\) - step2: Multiply the numbers: \(200+150\) - step3: Add the numbers: \(350\) Calculate or simplify the expression \( 72 * 10 + 15 * 7.50 \). Calculate the value by following steps: - step0: Calculate: \(72\times 10+15\times 7.5\) - step1: Multiply the numbers: \(720+15\times 7.5\) - step2: Multiply the numbers: \(720+112.5\) - step3: Add the numbers: \(832.5\) Calculate or simplify the expression \( 588 + 196 \). Calculate the value by following steps: - step0: Calculate: \(588+196\) - step1: Add the numbers: \(784\) Calculate or simplify the expression \( 41635.09378125 - 18000 \). Calculate the value by following steps: - step0: Calculate: \(41635.09378125-18000\) - step1: Subtract the numbers: \(23635.09378125\) Let's summarize the calculations step by step: ### 4.1. Commission from Selling Cakes **4.1.1.** Earnings from selling 20 packs of muffins and 20 packs of scones: - Total earnings from muffins: \[ 20 \times 10 = 200 \] - Total earnings from scones: \[ 20 \times 7.50 = 150 \] - Total earnings: \[ 200 + 150 = 350 \] - Total commission: \[ 2 \times (20 + 20) = 80 \] **4.1.2.** Earnings from selling 72 packs of muffins and 15 packs of scones: - Total earnings from muffins: \[ 72 \times 10 = 720 \] - Total earnings from scones: \[ 15 \times 7.50 = 112.50 \] - Total earnings: \[ 720 + 112.50 = 832.50 \] - Total commission: \[ 2 \times (72 + 15) = 174 \] **4.1.3.** If Anele sells only scones and earns R55.50 in commission: - Number of packs sold: \[ \frac{55.50}{2} = 27.75 \text{ (which means she sold 27 packs)} \] ### 4.2. Tool Hire Business **4.2.1.** Total hiring cost for Mr. Mabhande for 3 days: - Total hiring cost: \[ 135 \times 3 + 25 \times 3 + 2 \times 18 \times 3 = 588 \] **4.2.2.** Extra amount if he returns the tools one day late: - Total daily cost: \[ 588 \] - Extra amount for one day late: \[ 588 \] ### 4.3. Investment Calculation Diego invests R18000 for 6 years at 15% p.a. compounded annually: - Future Value (FV): \[ FV = 18000 \times (1 + 0.15)^6 \approx 41635.09 \] - Interest received: \[ 41635.09 - 18000 \approx 23635.09 \] ### Summary of Results - **4.1.1.** Total earnings from 20 packs of muffins and 20 packs of scones: **R350** - **4.1.2.** Total earnings from 72 packs of muffins and 15 packs of scones: **R832.50** - **4.1.3.** Number of scones sold for R55.50 commission: **27 packs** - **4.2.1.** Total hiring cost for 3 days: **R588** - **4.2.2.** Extra amount for one day late: **R588** - **4.3.** Future value of investment after 6 years: **R41635.09** - **Interest received:** **R23635.09** All answers are rounded to two decimal places where applicable.