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
You're on a roll — Here are the solutions to the problems: a) Step 1: Calculate Joshua's running rate. Joshua runs 48 km in 2 hours, so his rate is: Rate = 48 km2 hours = 24 km/hour He also runs 168 km in 7 hours, which gives the same rate: Rate = 168 km7 hours = 24 km/hour Step 2: Calculate the time taken to run 384 km. Using the formula Time = DistanceRate: Time = 384 km24 km/hour = 16 hours It will take Joshua 16 hours to run 384 km. 16 hours b) Step 1: Identify the fixed cost and variable cost. The cost of renting a party garden (fixed cost) is UGX 2,000,000. The cost of food per person (variable cost) is UGX 20,000. Step 2: Write the equation. Let C be the total cost and P be the number of people. C = 2,000,000 + 20,000P The equation connecting the total cost of the evening party with the number of people is C = 2,000,000 + 20,000P. c) Step 1: Substitute the number of people into the cost equation. For 20 people, P = 20. Using the 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 UGX 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. So, the total cost C must be less than or equal to this amount: 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 is able to invite is 150 people. Send me the next one 📸