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
a) Step 1: Calculate Joshua's running speed. Joshua's speed is consistent. Speed = DistanceTime Using the first record: Speed_1 = 48 km2 hours = 24 km/h Using the second record: Speed_2 = 168 km7 hours = 24 km/h Joshua's constant speed is 24 km/h. Step 2: Calculate the time it will take Joshua to run 384 km. Time = DistanceSpeed Time = 384 km24 km/h Time = 16 hours It will take Joshua 16 hours to run 384 km. The information about "from 2023 to 2026" is extraneous for this calculation, as the question asks for the time to run the distance, not the year he completes it. b) Step 1: Identify the fixed cost and the variable cost per person. Fixed cost (renting garden) = UGX 2,000,000 Cost per person (food) = UGX 20,000 Let C be the total cost and P be the number of people. Step 2: Write the equation connecting the total cost of the evening party with the number of people. C = 2,000,000 + 20,000P The equation is C = 2,000,000 + 20,000P. c) Step 1: Substitute the number of people into the cost equation. For 20 people, P = 20. C = 2,000,000 + 20,000(20) Step 2: Calculate the total cost. C = 2,000,000 + 400,000 C = 2,400,000 The total cost for 20 people is UGX 2,400,000. d) Step 1: Set up an inequality using the maximum budget. The maximum budget is UGX 5,000,000. 2,000,000 + 20,000P 5,000,000 Step 2: Solve the inequality for P. 20,000P 5,000,000 - 2,000,000 20,000P 3,000,000 P (3,000,000)/(20,000) P 150 Step 3: Determine the greatest number of people. Since the number of people must be a whole number, the greatest number of people the committee is able to invite is 150. The greatest number of people is 150. Send me the next one 📸