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.
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carol, let's knock this out. a) Find the total amount of money obtained from the sale of the land. Step 1: Identify the shares of each child. Let M be the total amount of money obtained from the sale of the land. Musa receives 25\% of M. Amina receives 30\% of M. Kato receives half of what Amina received, which is (1)/(2) × 30\% = 15\% of M. Sarah receives the remainder, which is 120,000,000 shillings. Step 2: Calculate the total percentage received by Musa, Amina, and Kato. 25\% + 30\% + 15\% = 70\% Step 3: Determine the percentage Sarah received. Since Sarah received the remainder, her share is 100\% - 70\% = 30\% of M. Step 4: Calculate the total amount of money M. We know that 30\% of M is 120,000,000 shillings. 0.30 × M = 120,000,000 M = (120,000,000)/(0.30) M = 400,000,000 shillings The total amount of money obtained from the sale of the land is 400,000,000 shillings. b) Find how much Musa, Amina, and Kato each received. Step 1: Calculate Musa's share. Musa received 25\% of M. 0.25 × 400,000,000 = 100,000,000 shillings Step 2: Calculate Amina's share. Amina received 30\% of M. 0.30 × 400,000,000 = 120,000,000 shillings Step 3: Calculate Kato's share. Kato received 15\% of M. 0.15 × 400,000,000 = 60,000,000 shillings Musa received 100,000,000 shillings, Amina received 120,000,000 shillings, and Kato received 60,000,000 shillings. c) Determine the next date when all four children will visit their parents on the same day. Step 1: Identify the visiting intervals for each child. Musa visits every 15 days. Amina visits every 18 days. Kato visits every 24 days. Sarah visits every 30 days. They all last visited on January 1st. Step 2: Find the Least Common Multiple (LCM) of the visiting intervals. We need to find the LCM of 15, 18, 24, and 30. Prime factorization: 15 = 3 × 5 18 = 2 × 3^2 24 = 2^3 × 3 30 = 2 × 3 × 5 The LCM is 2^3 × 3^2 × 5 = 8 × 9 × 5 = 360. So, they will all visit on the same day every 360 days. Step 3: Calculate the next common visit date. Their last common visit was January 1st. The next common visit will be 360 days after January 1st. Assuming the current year is a leap year (e.g., 2024), February has 29 days. Counting 360 days from January 1st: January: 31 days (remaining 360 - 31 = 329) February: 29 days (remaining 329 - 29 = 300) March: 31 days (remaining 300 - 31 = 269) April: 30 days (remaining 269 - 30 = 239) May: 31 days (remaining 239 - 31 = 208) June: 30 days (remaining 208 - 30 = 178) July: 31 days (remaining 178 - 31 = 147) August: 31 days (remaining 147 - 31 = 116) September: 30 days (remaining 116 - 30 = 86) October: 31 days (remaining 86 - 31 = 55) November: 30 days (remaining 55 - 30 = 25) December: The 25th day of December. The next date when all four children will visit their parents on the same day is December 25th. d) State whether the parents should organize the thanksgiving lunch before the end of March. Step 1: Recall the condition for organizing the lunch. The parents plan to organize a thanksgiving lunch only if the next common visit falls before the end of March. Step 2: Compare the next common visit date with the end of March. The next common visit date is December 25th. The end of March is March 31st. Step 3: Conclude based on the comparison. Since December 25th is after March 31st, the condition is not met. The parents should not organize the thanksgiving lunch before the end of March. What's next?