The partnership contract for Hanes and Jones LLP provides that Hanes is to receive a bonus of 20% of net income (after the bonus) and that the remaining net income is to be divided equally. If the partnership income before the bonus for the year is $57,600, Hanes’ share of this pre-bonus income is:

To find Hanes’ share of the pre-bonus income, we first need to calculate the amount of the bonus he receives, which is 20% of the net income after accounting for the bonus itself. Let's denote the net income after the bonus as "NI".

The bonus B can be expressed as: B = 20% * NI or B = 0.20 * NI

After the bonus is paid, the net income is the original income before the bonus minus the bonus itself: NI = $57,600 - B

Substituting the expression for B into the net income equation gives: NI = $57,600 - 0.20 * NI

Now we need to solve this equation for NI. Begin by distributing the 0.20 into NI: NI + 0.20 * NI = $57,600

Combine like terms by adding the NI and 0.20 * NI: 1 * NI + 0.20 * NI = 1.20 * NI = $57,600

Now divide both sides by 1.20 to solve for NI: NI = $57,600 / 1.20 NI = $48,000

Once we have the net income after the bonus, we can calculate the actual bonus amount, B: B = 0.20 * NI B = 0.20 * $48,000 B = $9,600

So, the net income after Hanes' bonus is $48,000, and his bonus is $9,600. To find Hanes' share of the pre-bonus income, we need to add his bonus to his part of the evenly divided net income after the bonus. Since the remaining net income is divided equally, we divide the after-bonus net income by 2 (as there are two partners, Hanes and Jones) to find out Hanes' share of that:

Hanes' share of the divided net income = NI / 2 Hanes' share of the divided net income = $48,000 / 2 Hanes' share of the divided net income = $24,000

Finally, to find Hanes’ total share, we combine his bonus with his share of the divided net income: Hanes' total share = Hanes' bonus + Hanes' share of the divided net income Hanes' total share = $9,600 + $24,000 Hanes' total share = $33,600

Therefore, Hanes' share of the pre-bonus income is $33,600.

Extra: In a partnership, partners may agree to distribute profits in various ways, and one such way is the inclusion of a bonus for specific partners. This bonus can be a predetermined flat amount or a percentage of profits. After bonuses are allocated, the remaining profits are then divided as per the partnership agreement, which could be equally among partners or in another agreed-upon ratio.

The calculation involving the determination of a bonus based on a percentage of net income after the bonus is a common type of profit-sharing arrangement. It requires an understanding of algebraic manipulation to solve for the unknown net income. This real-world application of algebra illustrates how mathematical concepts can be used to solve problems in fields like accounting and business.