1. **State the problem:** We have a building with 26 apartments of sizes 90, 120, 140, and 150 m². The number of 120 m² apartments is $x$, and the number of 90 m² apartments is unknown. There are 8 apartments of 140 m² and 5 apartments of 150 m². 2. **Given data:** - Total apartments: 26 - Number of 140 m² apartments: 8 - Number of 150 m² apartments: 5 - Total monthly collection from all apartments: 6440 - Collection from 140 and 150 m² apartments: 3740 3. **Find:** (a) The total size in m² of the apartments that pay 3740. (b) The payment per m². (c) The payment for a 150 m² apartment. --- ### Step 1: Find the total number of apartments sized 90 and 120 m² Since total apartments are 26, and 8 + 5 = 13 are 140 and 150 m², $$x + \text{number of 90 m² apartments} = 26 - 13 = 13$$ Let the number of 90 m² apartments be $y$, then: $$x + y = 13$$ --- ### Step 2: Find the total size of apartments paying 3740 The 140 m² apartments: 8 apartments The 150 m² apartments: 5 apartments Total size: $$8 \times 140 + 5 \times 150 = 1120 + 750 = 1870 \text{ m}^2$$ **Answer (a):** $1870$ m² --- ### Step 3: Find the payment per m² Total payment from these apartments is 3740. Payment per m²: $$\frac{3740}{1870} = 2$$ **Answer (b):** 2 (payment units per m²) --- ### Step 4: Find the payment for a 150 m² apartment Payment per apartment: $$150 \times 2 = 300$$ **Answer (c):** 300 --- ### Summary: - (a) Total size of apartments paying 3740: **1870 m²** - (b) Payment per m²: **2** - (c) Payment for a 150 m² apartment: **300**