Explanation:
To determine how much more Sarah would have received if the money was shared out immediately after her birthday instead of today, we need to consider the difference in their ages at the time of sharing.Currently, James is 8 years old, Sarah is 6 years old, and Lucy is 4 years old. Let's calculate the ratio of their ages:James:Sarah:Lucy = 8:6:4To find the total number of parts in the ratio, we add up the individual parts: 8 + 6 + 4 = 18.Now, let's calculate the share of each grandchild based on the ratio:James' share = (8/18) * $270
Sarah's share = (6/18) * $270
Lucy's share = (4/18) * $270Now, since Sarah's birthday is in three weeks and Lucy's birthday is next week, we need to calculate their ages after their respective birthdays.After three weeks, Sarah will turn 7 years old, and Lucy will turn 5 years old. Let's recalculate the ratio based on their ages after their birthdays:James:Sarah:Lucy = 8:7:5Again, let's calculate the total number of parts in the new ratio: 8 + 7 + 5 = 20.Now, let's calculate their shares based on the new ratio:James' share = (8/20) * $270
Sarah's share = (7/20) * $270
Lucy's share = (5/20) * $270To determine how much more Sarah would have received, we need to find the difference between her share today and her share after her birthday:Difference in Sarah's share = Sarah's share after her birthday - Sarah's share todayNow we can calculate:Sarah's share after her birthday = (7/20) * $270
Sarah's share today = (6/18) * $270Difference in Sarah's share = (7/20) * $270 - (6/18) * $270Calculating this difference will give us the amount Sarah would have received more if the money was shared after her birthday instead of today.