Answer: Therefore, the ratio of A's total share of the profit to B's is approximately 1.1333... or approximately 1.13:1.
Step-by-step explanation:
To determine the ratio of A's total share of the profit to B's, we need to calculate the individual shares of both A and B.
Let's start by finding A's share:
A contributes $14,000 to the partnership.
A receives 20% of the profit as a manager. Let's denote the profit as P.
A's share as a manager = 20% of P = 0.2P
The remaining profit after A's manager share will be divided based on the capital ratio.
A's capital = $14,000
B's capital = $18,000
Total capital = $14,000 + $18,000 = $32,000
A's share based on capital = (A's capital / Total capital) * (Profit - A's manager share)
= ($14,000 / $32,000) * (P - 0.2P)
= $0.4375P
Now, let's find B's share:
B contributes $18,000 to the partnership.
B's share based on capital = (B's capital / Total capital) * (Profit - A's manager share)
= ($18,000 / $32,000) * (P - 0.2P)
= $0.5625P
To find the ratio of A's total share of the profit to B's, we divide A's total share by B's total share:
(A's manager share + A's share based on capital) / B's share based on capital
(A's manager share + A's share based on capital) / B's share based on capital
= (0.2P + $0.4375P) / $0.5625P
= (0.6375P) / (0.5625P)
= 1.1333...