Determine how much pocket money will each child get. Determine the amount paid for a child in the; first installment, second installment. When is he likely to have a meeting and a follow up visit at the same time?

Here are the solutions for Item 1. Item 1: a) Determine how much pocket money each child will get. Step 1: Calculate the total sum of the children's ages. The ages are 5, 10, 12, and 13 years. Sum of ages = 5 + 10 + 12 + 13 = 40 Step 2: Calculate the value of one ratio part. The total pocket money is Shs 520,000. Value per ratio part = Total pocket moneySum of ages = (520,000)/(40) = 13,000 Shs Step 3: Calculate the pocket money for each child. Child 1 (5 years old): 5 × 13,000 = 65,000 Shs Child 2 (10 years old): 10 × 13,000 = 130,000 Shs Child 3 (12 years old): 12 × 13,000 = 156,000 Shs Child 4 (13 years old): 13 × 13,000 = 169,000 Shs b) Determine the amount paid for a child in the: (i) first installment (ii) second installment Step 1: Let T be the total school fees for a child. Set up an equation based on the installment payments. First installment = 60\% of T = 0.60T Remaining amount after first installment = T - 0.60T = 0.40T Second installment = (2)/(3) of the remaining amount = (2)/(3) × 0.40T = (0.80)/(3)T Third installment = Shs 160,000 The sum of the installments equals the total fees: T = 0.60T + (0.80)/(3)T + 160,000 Step 2: Solve the equation for T. T - 0.60T - (0.80)/(3)T = 160,000 0.40T - (0.80)/(3)T = 160,000 Multiply by 3 to clear the fraction: 3 × 0.40T - 0.80T = 3 × 160,000 1.20T - 0.80T = 480,000 0.40T = 480,000 T = (480,000)/(0.40) = 1,200,000 Shs The total school fees for a child is Shs 1,200,000. Step 3: Calculate the first installment. First installment = 0.60 × 1,200,000 = 720,000 Shs Step 4: Calculate the second installment. Remaining amount = 1,200,000 - 720,000 = 480,000 Shs Second installment = (2)/(3) × 480,000 = 320,000 Shs c) When is he likely to have a meeting and a follow up visit at the same time? Step 1: Determine the frequency of each event. Follow-up visits occur every 21 days. Weekly meetings occur every 7 days. Step 2: Find the least common multiple (LCM) of the frequencies to determine when they coincide. LCM(21, 7) = 21 days This means both events will coincide every 21 days. Step 3: Calculate the next date of coincidence. The last coincidence was on 11/05/2025. Add 21 days to this date. May has 31 days. 11 (May) + 21 days = 32 days into May Since May has 31 days, 32 - 31 = 1. The next coincidence will be on 01/06/2025. That's 2 down. 3 left today — send the next one.