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
Step 1: Define variables for the number of trips. Let B be the number of trips made by the bus. Let M be the number of trips made by the matatu. Step 2: Formulate equations based on the given information. The bus has a capacity of 33 people. The matatu has a capacity of 11 people. The total number of people transported is 319. So, the total people transported can be expressed as: 33B + 11M = 319 (1) The matatu made one extra trip than the bus: M = B + 1 (2) Step 3: Substitute equation (2) into equation (1) and solve for B. Substitute M = B + 1 into 33B + 11M = 319: 33B + 11(B + 1) = 319 33B + 11B + 11 = 319 44B + 11 = 319 44B = 319 - 11 44B = 308 B = (308)/(44) B = 7 Step 4: Calculate the number of trips made by the matatu. Using M = B + 1: M = 7 + 1 M = 8 Step 5: Calculate the number of people transported by the matatu. The matatu transported 11 people per trip and made 8 trips. Number of people transported by matatu = 11 × M 11 × 8 = 88 The matatu transported 88 people. 88 people