✅ First, set up equations based on the given conditions: J = (3/5)K, L = (1/2)(J + K), and K = J + 300.

Substitute K = J + 300 into the first equation to solve for J: J = (3/5)(J + 300) which simplifies to 5J = 3J + 900, yielding 2J = 900, so J = 450.

Then, find Kevin's share: K = J + 300 = 450 + 300 = 750.

Next, calculate Liam's share: L = (1/2)(J + K) = (1/2)(450 + 750) = (1/2)(1200) = 600.

Finally, sum the individual shares to find the total prize money: Total = J + K + L = 450 + 750 + 600 = 1800.

❌ Option B ($1575) is incorrect because it might result from calculating Liam's share as half of Kevin's share only (L = 1/2 * K = 1/2 * 750 = 375), leading to a total of 450 + 750 + 375 = 1575.

❌ Option C ($1425) is incorrect because it might result from calculating Liam's share as half of John's share only (L = 1/2 * J = 1/2 * 450 = 225), leading to a total of 450 + 750 + 225 = 1425.

❌ Option D ($1950) is incorrect because it could arise if Liam's share was mistakenly assumed to be equal to Kevin's share (L = K = 750), leading to a total of 450 + 750 + 750 = 1950.

✅ Let the total prize money be T. Let A, B, and C be the shares of Alex, Ben, and Chloe, respectively. So, A + B + C = T.

From the first condition, "Alex received 3/5 of what Ben and Chloe together received": . This implies . Since , we have , which simplifies to , so , meaning .

From the second condition, "Ben received 2/5 of what Alex and Chloe together received": . This implies . Since , we have , which simplifies to , so , meaning .

Now, we find Chloe's share (C) as a fraction of the total: . To combine these, find a common denominator for 8 and 7, which is 56. .

The third condition states, "Chloe received $1200 less than Alex", which means . Substitute the fractional values: . Convert (3/8)T to a fraction with denominator 56: .

This simplifies to , or . Therefore, .

Formula(s) used:

• Ratio:
• Proportion:
• Sharing formula (derived): If an individual's share A is times the sum of other shares, , and total , then .

❌ Option B is incorrect. This would result if the fractional difference was mistakenly calculated as of the total instead of (i.e., ).

❌ Option C is incorrect. This value might arise from various calculation errors, such as mistakenly using as the fraction of the total for the $1200 difference, which would give .

❌ Option D is incorrect. This value of $31,200 would occur if the multiplier was 26 instead of 28 (), possibly from an arithmetic error during the simplification of fractions or solving the equation.