If a salesperson wishes to earn a net income of $120,000 and total expenses are 45% of earnings, what gross income should they aim for?

To determine the gross income necessary for a salesperson to achieve a desired net income of $120,000 with total expenses representing 45% of their earnings, we start by understanding the relationship between gross income, expenses, and net income.

Gross income can be defined as the total income before any expenses are deducted. To find the needed gross income, we consider that if expenses are 45% of the gross income, then the salesperson keeps 55% of their gross income after expenses.

The formula can be framed as follows:

1. Let ( G ) denote the gross income.

2. Since expenses are 45% of gross income, the expenses can be expressed as ( 0.45G ).

3. The net income, which is what's left after expenses, will then be ( G - 0.45G = 0.55G ).

To solve for the gross income in relation to the desired net income:

• Set the net income equal to ( 0.55G ) and substitute the desired net income of $120,000 into the equation:

[

0.55G = 120,000

]

• To find ( G ), divide both sides by 0.55: