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's the solution to the problem: a) To find how much profit Moses re-invested, we first determine the ratio of their contributions. Step 1: Determine the ratio of contributions. Sarah's contribution: Shs 4,000,000 Moses's contribution: Shs 6,000,000 The ratio of Sarah's contribution to Moses's contribution is: 4,000,000 : 6,000,000 = 4 : 6 = 2 : 3 The total number of ratio parts is 2 + 3 = 5. Step 2: Calculate Moses's share of the profit. Total profit made: Shs 1,500,000 Moses's share of the profit is (3)/(5) of the total profit. Moses's profit share = (3)/(5) × 1,500,000 Moses's profit share = 3 × 300,000 Moses's profit share = 900,000 Since they re-invested the entire profit, Moses re-invested his share. The amount of profit Moses re-invested in the business is Shs 900,000. b) To find the percentage increase in the number of birds, we use the formula for percentage increase. Step 1: Calculate the increase in the number of birds. Initial number of birds: 2,000 New number of birds: 2,500 Increase in birds = 2,500 - 2,000 = 500 Step 2: Calculate the percentage increase. Percentage increase = IncreaseOriginal number × 100\% Percentage increase = (500)/(2,000) × 100\% Percentage increase = (1)/(4) × 100\% Percentage increase = 25\% The percentage increase in the number of birds was 25\%. c) To find the date when they would buy feeds and balance their books on the same day, we need to find the least common multiple (LCM) of the frequencies. Step 1: Identify the frequencies for each activity. Feeds are bought every 7 days. Books are balanced every 15 days. Step 2: Find the LCM of 7 and 15. Since 7 and 15 are coprime (they have no common factors other than 1), their LCM is their product. LCM(7, 15) = 7 × 15 = 105 days This means both events will coincide every 105 days. Step 3: Calculate the future date by adding 105 days to the starting date (March 1, 2024). Starting date: March 1, 2024. Number of days in March 2024 (a leap year, but March is unaffected): 31 days. Days remaining in March after March 1: 31 - 1 = 30 days. Remaining days to add: 105 - 30 = 75 days. Number of days in April: 30 days. Remaining days to add: 75 - 30 = 45 days. Number of days in May: 31 days. Remaining days to add: 45 - 31 = 14 days. The remaining 14 days fall in June. So, the date will be June 14, 2024. They would buy the feeds and also balance their books of accounts on the same day on June 14, 2024. Last free one today — make it count tomorrow, or type /upgrade for unlimited.