Katherine, Corey, and Joel invest $23,000, $9,000, and $16,000, respectively, to build a boat. After the boat was built, Katherine decided to sell her share of the investment to Corey and Joel. How much would Corey and Joel have to pay Katherine if they want to maintain the same ratio of their investments in the boat? a. How much would Corey would have to pay? b. How much would Joel have to pay?
The correct answer and explanation is:
Let’s break down the problem step-by-step.
Given:
- Katherine’s investment = $23,000
- Corey’s investment = $9,000
- Joel’s investment = $16,000
Katherine sells her entire share ($23,000) to Corey and Joel, but Corey and Joel want to maintain the same ratio of investments between themselves after buying Katherine’s share.
Step 1: Understand the current ratio between Corey and Joel
- Corey : Joel = $9,000 : $16,000
- Simplify the ratio by dividing both sides by 1,000: 9 : 16
Step 2: After buying Katherine’s share
- Total investment is still $23,000 + $9,000 + $16,000 = $48,000
- Katherine’s $23,000 share will be split between Corey and Joel in the ratio 9:16.
Step 3: Find how much of the $23,000 each would pay
- Total parts in ratio = 9 + 16 = 25 parts
- Corey’s share of Katherine’s $23,000 = (9/25) × $23,000 = $8,280
- Joel’s share of Katherine’s $23,000 = (16/25) × $23,000 = $14,720
Step 4: Final investments of Corey and Joel
- Corey’s new investment = original $9,000 + $8,280 = $17,280
- Joel’s new investment = original $16,000 + $14,720 = $30,720
Final answer:
a. Corey would have to pay $8,280
b. Joel would have to pay $14,720
Explanation:
The key to this problem is understanding that Katherine’s investment is being divided between Corey and Joel proportionally to their original investments. This keeps the ratio of their investments constant at 9:16. If Corey and Joel buy Katherine’s share in any other way, their ownership proportions would shift, which they want to avoid.
By dividing Katherine’s $23,000 according to the ratio 9:16, Corey pays less than Joel because his original investment was smaller. The calculations maintain fairness and preserve their relative stakes in the boat after Katherine exits the partnership.
This approach ensures that the combined investments of Corey and Joel sum to the full original investment ($48,000), but their individual contributions remain proportional.