Mark and Janet buy gold coins costing R 435000 . Mark contributes R163 12 Janet contributes the balance. How many coins should each receive based on ratio split if there are 24 coins altogether?

To determine how many gold coins Mark and Janet should receive based on their contributions, let's break down the problem step by step. ### **1. Understanding the Contributions** - **Total Cost of Coins:** R435,000 - **Mark's Contribution:** R16,312 - **Janet's Contribution:** \[ R435,000 - R16,312 = R418,688 \] ### **2. Calculating the Ratio of Contributions** The ratio of Mark's contribution to Janet's contribution is: \[ \text{Mark} : \text{Janet} = 16,312 : 418,688 \] To simplify this ratio, divide both numbers by their greatest common divisor (GCD), which is 8: \[ \frac{16,312}{8} : \frac{418,688}{8} = 2,039 : 52,336 \] ### **3. Distributing the 24 Coins** Given the simplified ratio of 2,039 : 52,336, we need to distribute 24 coins proportionally. First, find the total parts: \[ 2,039 + 52,336 = 54,375 \text{ parts} \] Next, determine the number of coins each should receive: - **Mark's Share:** \[ \frac{2,039}{54,375} \times 24 \approx 0.9 \text{ coins} \] - **Janet's Share:** \[ \frac{52,336}{54,375} \times 24 \approx 23.1 \text{ coins} \] ### **4. Final Allocation** Since coins can't be split into fractions in a practical scenario: - **Mark receives:** 1 coin - **Janet receives:** 23 coins This allocation ensures that both Mark and Janet receive whole coins proportional to their financial contributions. **Final Answer:** Mark should receive 1 coin and Janet should receive 23 coins out of the 24 total.