Exercise 1.22 1 Divide R200 between you and your friend in the ratio \( 3: 2 \). 2. Divide R240 in the ratio \( 3: 4: 5 \). 3. Three investors buy shares in a cellphone business. Senzi invests R1 000 , Neo invests R1 500 and Thabo 16500 . A year later they receive thelr firsi dividend (pay-out) of R1 500 . How must they share the dividend?

Let's solve each part of Exercise 1.22 step by step. --- ### **1. Divide R200 between you and your friend in the ratio \( 3:2 \).** **Step 1:** Determine the total number of parts in the ratio. \[ 3 + 2 = 5 \text{ parts} \] **Step 2:** Calculate the value of one part. \[ \text{Value of one part} = \frac{200}{5} = R40 \] **Step 3:** Divide the money based on the ratio. - **Your share:** \( 3 \times R40 = R120 \) - **Friend's share:** \( 2 \times R40 = R80 \) **Answer:** - You receive **R120** - Your friend receives **R80** --- ### **2. Divide R240 in the ratio \( 3:4:5 \).** **Step 1:** Determine the total number of parts in the ratio. \[ 3 + 4 + 5 = 12 \text{ parts} \] **Step 2:** Calculate the value of one part. \[ \text{Value of one part} = \frac{240}{12} = R20 \] **Step 3:** Divide the money based on the ratio. - **First person's share:** \( 3 \times R20 = R60 \) - **Second person's share:** \( 4 \times R20 = R80 \) - **Third person's share:** \( 5 \times R20 = R100 \) **Answer:** - First person receives **R60** - Second person receives **R80** - Third person receives **R100** --- ### **3. Three investors (Senzi, Neo, and Thabo) invest R1,000, R1,500, and R16,500 respectively. They receive a dividend of R1,500. How should the dividend be shared?** **Step 1:** Calculate the total investment. \[ R1,000 + R1,500 + R16,500 = R19,000 \] **Step 2:** Determine each investor's share of the total investment. - **Senzi's share:** \( \frac{1,000}{19,000} \) - **Neo's share:** \( \frac{1,500}{19,000} \) - **Thabo's share:** \( \frac{16,500}{19,000} \) **Step 3:** Calculate each investor's dividend. - **Senzi's dividend:** \[ \frac{1,000}{19,000} \times 1,500 = \frac{1,500,000}{19,000} \approx R78.95 \] - **Neo's dividend:** \[ \frac{1,500}{19,000} \times 1,500 = \frac{2,250,000}{19,000} \approx R118.42 \] - **Thabo's dividend:** \[ \frac{16,500}{19,000} \times 1,500 = \frac{24,750,000}{19,000} \approx R1,302.63 \] **Answer:** - **Senzi** receives approximately **R78.95** - **Neo** receives approximately **R118.42** - **Thabo** receives approximately **R1,302.63** *Note: The slight discrepancies in decimal places are due to rounding.*