If $360 is shared in the ratio 2:3:9, what is the difference between the largest and smallest shares?

• A. $120
• B. $180
• C. $280
• D. $300

Answer: (C)

To solve the problem of sharing $360 in the ratio 2:3:9, we first need to determine the total parts in the ratio. By adding the parts together:

2 + 3 + 9 = 14 parts.

Next, we calculate the value of one part by dividing the total amount by the total number of parts:

$360 ÷ 14 = $25.71 (approximately).

Now we can find the individual shares based on the ratio:

1. The first share is 2 parts:

2 × $25.71 ≈ $51.43.

2. The second share is 3 parts:

3 × $25.71 ≈ $77.14.

3. The third share is 9 parts:

9 × $25.71 ≈ $228.57.

The smallest share is approximately $51.43, and the largest share is approximately $228.57.

To find the difference between the largest and smallest shares, we subtract the value of the smallest share from the largest share:

$228.57 - $51.43 ≈ $177.14.

This is not matching with the provided answer, indicating a potential discrepancy in the calculated shares