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
Welcome back Mudiba — missed you this week. Here are the solutions to your questions: Task (a): Step 1: Determine the time taken for all data entrants to finish a learner's data simultaneously. Data entrant A takes 10 minutes per learner. Data entrant B takes 15 minutes per learner. Data entrant C takes 10 minutes per learner. To find when they all finish at the same time, we need to find the Least Common Multiple (LCM) of their individual times. LCM(10, 15, 10) = LCM(10, 15) Prime factorization of 10 is 2 × 5. Prime factorization of 15 is 3 × 5. LCM(10, 15) = 2 × 3 × 5 = 30 minutes So, they will all finish a batch of learners simultaneously every 30 minutes. a) (i) At what time will all the data entrants get a break together? They started working at 8:30 am. The first break will occur after 30 minutes. 8:30 am + 30 minutes = 9:00 am The data entrants will get a break together at 9:00 am. a) (ii) Obtain the number of learners whose data was captured before the first break. The duration before the first break is 30 minutes. Number of learners captured by A: 30 minutes10 minutes/learner = 3 learners Number of learners captured by B: 30 minutes15 minutes/learner = 2 learners Number of learners captured by C: 30 minutes10 minutes/learner = 3 learners Total number of learners captured: 3 + 2 + 3 = 8 learners The total number of learners whose data was captured before the first break is 8 learners. Task (b): Step 1: Identify the relevant financial information. School fees per learner: Ugx. 900,000. Cost for refreshments for guests per learner: Ugx. 5,000. Percentage of remaining fees for food: 40%. b) (i) Determine how much money the school spent on refreshments if it was based on the learners whose data was captured before the first break. From part (a)(ii), 8 learners had their data captured before the first break. Cost for refreshments per learner: Ugx. 5,000. Total money spent on refreshments: 8 learners × Ugx. 5,000/learner = Ugx. 40,000 The school spent Ugx. 40,000 on refreshments. b) (ii) How much money did each learner pay on food. First, calculate the remaining fees per learner after deducting the guest refreshments. Remaining fees per learner = Total fees per learner - Guest refreshments per learner Ugx. 900,000 - Ugx. 5,000 = Ugx. 895,000 Next, calculate 40% of these remaining fees for food. Money for food per learner = 40\% × Ugx. 895,000 0.40 × Ugx. 895,000 = Ugx. 358,000 Each learner paid Ugx. 358,000 on food. Send me the next one 📸