Final answer:
The total sum of money shared among three people in the ratio of 15:18:7 is 22800, the smallest share is 3990, which corresponds to option d, and the largest share is 10260.
Step-by-step explanation:
To determine the total sum of money and the largest share when a sum of money is shared among three people in the ratio of 15:18:7, first we add the parts of the ratio together to find the total number of parts into which the sum of money is divided. We have 15 parts + 18 parts + 7 parts = 40 parts.
Given that the smallest share corresponds to the 7 parts of the total and we have four different options for the smallest share (a: 84, b: 133, c: 301, d: 3990), we must divide each option by 7 to see which one results in a whole number when multiplied by the total number of parts, 40. Through this process, option d: 3990 is the correct smallest share as 3990 ÷ 7 = 570, and then 570 multiplied by the total number of parts, 40, gives us a total sum of 22800.
To find the largest share, we take the 18 parts of the person with the largest share, multiply by 570, and get the largest share to be 10260.
Therefore, the correct option for the smallest share is d: 3990, the total sum is 22800, and the largest share is 10260.