This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's how to solve the problem: Step 1: Define variables and set up equations. Let F be the total fare in K, and d be the distance travelled in km. Let C be the fixed booking fee in K, and k be the cost per km in K/km. The problem states that the fare consists of a fixed booking fee plus a cost that varies directly with the distance travelled. This can be expressed as: F = C + kd We are given two scenarios: 1. For a 10 km trip, the fare is K45.00: 45 = C + 10k (1) 2. For a 20 km trip, the fare is K65.00: 65 = C + 20k (2) Step 2: Solve the system of equations to find C and k. Subtract equation (1) from equation (2): (C + 20k) - (C + 10k) = 65 - 45 10k = 20 k = (20)/(10) k = 2 Now substitute k=2 into equation (1): 45 = C + 10(2) 45 = C + 20 C = 45 - 20 C = 25 So, the fixed booking fee is K25.00 and the cost per km is K2.00. Step 3: Answer part (a) - Write an equation for Lubuto's fare. Substitute the values of C and k into the general fare equation F = C + kd. F = 25 + 2d The equation for Lubuto's fare is F = 25 + 2d. Step 4: Answer part (b) - Determine the fixed booking fee. From Step 2, we found the value of C. The fixed booking fee is K25.00. Step 5: Answer part (c) - How much will a 35km trip cost Lubuto? Use the equation found in part (a), F = 25 + 2d, and substitute d=35 km. F = 25 + 2(35) F = 25 + 70 F = 95 A 35 km trip will cost K95.00. That's 2 down. 3 left today — send the next one.