(5) A truck carries a load of 50 boxes; some are 20 kg boxes and the rest are 25 kg boxes. If the total weight of all boxes is 1175 kg , how many of each type are there? (6) The cost of producing pens with the company logo printed on them consists of a one time setup fee of Birr 1000 plus Birr 20 for each pen produced. Determine the number of pens produced with a cost of Birr 5,000 pens.

Let's solve each problem step by step. ### Problem (5) Let: - \( x \) = number of 20 kg boxes - \( y \) = number of 25 kg boxes We have the following equations based on the problem statement: 1. The total number of boxes: \[ x + y = 50 \] 2. The total weight of the boxes: \[ 20x + 25y = 1175 \] Now, we can solve these equations. From the first equation, we can express \( y \) in terms of \( x \): \[ y = 50 - x \] Now, substitute \( y \) in the second equation: \[ 20x + 25(50 - x) = 1175 \] Expanding this: \[ 20x + 1250 - 25x = 1175 \] Combining like terms: \[ -5x + 1250 = 1175 \] Subtracting 1250 from both sides: \[ -5x = 1175 - 1250 \] \[ -5x = -75 \] Dividing by -5: \[ x = 15 \] Now, substitute \( x \) back into the equation for \( y \): \[ y = 50 - 15 = 35 \] So, the solution is: - Number of 20 kg boxes: **15** - Number of 25 kg boxes: **35** ### Problem (6) The cost of producing pens consists of a one-time setup fee and a variable cost per pen. The total cost can be expressed as: \[ \text{Total Cost} = \text{Setup Fee} + (\text{Cost per Pen} \times \text{Number of Pens}) \] Given: - Setup Fee = Birr 1000 - Cost per Pen = Birr 20 - Total Cost = Birr 5000 We can set up the equation: \[ 5000 = 1000 + 20n \] Where \( n \) is the number of pens produced. Now, we can solve for \( n \): \[ 5000 - 1000 = 20n \] \[ 4000 = 20n \] Dividing both sides by 20: \[ n = \frac{4000}{20} = 200 \] So, the number of pens produced is **200**.