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 are the solutions to the math problems: a) After how many hours will it take Joshua to run the 384 km? Step 1: Calculate Joshua's speed. From the first record: Speed_1 = DistanceTime = 48 km2 hours = 24 km/hour From the second record: Speed_2 = DistanceTime = 168 km7 hours = 24 km/hour Joshua's consistent speed is 24 km/hour. Step 2: Calculate the time to run 384 km. Time = DistanceSpeed = 384 km24 km/hour = 16 hours It will take Joshua 16 hours to run 384 km. The information about "from 2023 to 2026" is irrelevant for this calculation. b) Write down the equation connecting the total cost of the evening party with the number of people. Step 1: Identify fixed and variable costs. Fixed cost (renting garden) = UGX 2,000,000 Variable cost per person (food) = UGX 20,000 Let C be the total cost and P be the number of people. Step 2: Formulate the equation. C = 2,000,000 + 20,000P The equation is C = 2,000,000 + 20,000P. c) Find the total cost for the 20 people attend. Step 1: Substitute P=20 into the cost equation from part (b). 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) Find the greatest number of the people the committee is able to invite. 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. Subtract 2,000,000 from both sides: 20,000P 5,000,000 - 2,000,000 20,000P 3,000,000 Divide by 20,000: P (3,000,000)/(20,000) P 150 The greatest number of people the committee can invite is 150 people. What's next?