At a new job selling high-end clothing to women, you earn 6...

At a new job selling high-end clothing to women, you earn $6 \%$ commission on all sales you make after the first $\$ 500$. Your pay can be represented by $p=0.06(s-500)$ dollars, where $s$ is the amount of sales you make in dollars. a. How much total pay will you earn from $\$ 2000$ in sales? b. How much total pay will you earn from $\$ 5000$ in sales? c. If you need at least $\$ 450$ per week to pay your bills, what sales do you have to make per week?

At a new job selling high-end clothing to women, you earn $6 \%$ commission on all sales you make after the first $\$ 500$. Your pay can be represented by $p=0.06(s-500)$ dollars, where $s$ is the amount of sales you make in dollars.
a. How much total pay will you earn from $\$ 2000$ in sales?
b. How much total pay will you earn from $\$ 5000$ in sales?
c. If you need at least $\$ 450$ per week to pay your bills, what sales do you have to make per week?

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Key Concepts

Commission-Based Compensation

Commission-based compensation is a pay structure where earnings are determined by the percentage of sales made, rather than a fixed salary. This system often includes a threshold amount of sales that must be met before earning commission, incentivizing employees to exceed a basic sales target and thus enhancing overall performance.

Linear Functions

Linear functions are mathematical expressions that illustrate a constant rate of change between two variables. In the context of sales and commission, the relationship between sales amount and earnings can be modeled by a linear equation, where the slope represents the commission rate and adjustments are made for any fixed thresholds or base amounts.

Inequalities and Solving for Variables

Inequalities are used to determine the range of values for a variable that meet a certain condition, such as earning a minimum amount. Solving an inequality derived from a linear equation allows one to identify the minimum sales needed to ensure that earnings reach or exceed a specified financial goal.

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