An air conditioning company sells two types of air conditioners: portable and wall mounted. The prices of these air cons are in the ratio. \( 2: 3 \). The price of a portable air con is cheaper. If the company sells 9 portable air cons and 11 wall mounted air cons and receives an income of R204 000, what is the price of each air con type?

Let's solve the problem step-by-step. 1. **Define Variables:** - Let \( k \) be the common multiplier for the prices. - Price of a **portable air conditioner** = \( 2k \) - Price of a **wall-mounted air conditioner** = \( 3k \) 2. **Set Up the Equation:** The total income from selling the air conditioners is given by: \[ \text{Total Income} = (\text{Number of Portable ACs} \times \text{Price of Portable AC}) + (\text{Number of Wall-Mounted ACs} \times \text{Price of Wall-Mounted AC}) \] Plugging in the numbers: \[ 204,000 = 9 \times 2k + 11 \times 3k \] \[ 204,000 = 18k + 33k \] \[ 204,000 = 51k \] 3. **Solve for \( k \):** \[ k = \frac{204,000}{51} = 4,000 \text{ R} \] 4. **Find the Prices:** - **Portable Air Conditioner:** \[ 2k = 2 \times 4,000 = 8,000 \text{ R} \] - **Wall-Mounted Air Conditioner:** \[ 3k = 3 \times 4,000 = 12,000 \text{ R} \] **Conclusion:** - **Portable Air Conditioner:** 8,000 R each - **Wall-Mounted Air Conditioner:** 12,000 R each