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 and set up equations based on the given information. Let C be the fare for a child and T be the fare for a teacher. From the problem, the fare for a school child is half the fare for a teacher: C = (1)/(2)T T = 2C For the first excursion, 120 children and 15 teachers paid a total of GH¢180. The total fare equation is: 120C + 15T = 180 Step 2: Solve for the fare of a child (C). Substitute T = 2C into the total fare equation: 120C + 15(2C) = 180 120C + 30C = 180 150C = 180 C = (180)/(150) C = (18)/(15) C = (6)/(5) C = 1.20 The fare for a child is GH¢1.20. i) The fare for a child is GH¢1.20. Step 3: Calculate the fare for a teacher (T). Using T = 2C: T = 2 × 1.20 T = 2.40 The fare for a teacher is GH¢2.40. Step 4: Solve for the number of children in the second scenario. For the second scenario, 20 teachers would go on an excursion with a total fare of GH¢240.00. Let N_c be the number of children. The total fare equation for this scenario is: N_c C + 20T = 240 Substitute the values of C = 1.20 and T = 2.40: N_c (1.20) + 20(2.40) = 240 1.20 N_c + 48 = 240 1.20 N_c = 240 - 48 1.20 N_c = 192 N_c = (192)/(1.20) N_c = (1920)/(12) N_c = 160 ii) The number of children who would go on the excursion is 160. Send me the next one 📸