Final answer:
To find the difference between the largest and smallest shares, divide the total amount by the sum of the ratio parts and then find the value of each share by multiplying the number of parts by the result. Finally, subtract the value of the smallest share from the value of the largest share to find the difference.
Step-by-step explanation:
To find the difference between the largest and smallest shares, we need to determine the value of each share. First, we add up the parts of the ratio: 2 + 3 + 9 = 14. Next, we divide the total amount of $560 by 14 to find the value of 1 part: $560 ÷ 14 = $40. Now, we can find the value of each share by multiplying the number of parts in the ratio by $40. The largest share is 9 parts, so its value is 9 × $40 = $360. The smallest share is 2 parts, so its value is 2 × $40 = $80. Therefore, the difference between the largest and smallest shares is $360 - $80 = $280.