Each week Sally, a salesperson in Eddie's Electronic...

Each week Sally, a salesperson in Eddie's Electronic Emporium, receives a base pay of $\$ 300$ plus a commission on the dollar amount of her sales. During any week when the total value of her sales is $\$ 5,000$ or less, her commission is 10$\% .$ During those weeks when the total value of her sales exceeds $\$ 5,000,$ her commission is 12$\%$ of the entire amount. Last year during the first week of February, she earned $\$ 1,080 .$ What was the total value of her sales that week? $$\begin{array}{l}{\text { (A) } \$ 5,400} \\ {\text { (B) } \$ 6,500} \\ {\text { (C) } \$ 7,500} \\ {\text { (D) } \$ 9,000}\end{array}$$

Each week Sally, a salesperson in Eddie's Electronic Emporium,
receives a base pay of $\$ 300$ plus a commission on the dollar
amount of her sales. During any week when the total value of her
sales is $\$ 5,000$ or less, her commission is 10$\% .$ During those weeks when the total value of her sales exceeds $\$ 5,000,$ her
commission is 12$\%$ of the entire amount. Last year during the
first week of February, she earned $\$ 1,080 .$ What was the total
value of her sales that week?
$$\begin{array}{l}{\text { (A) } \$ 5,400} \\ {\text { (B) } \$ 6,500} \\ {\text { (C) } \$ 7,500} \\ {\text { (D) } \$ 9,000}\end{array}$$

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Key Concepts

Piecewise Functions

This concept involves defining a function by multiple sub-functions, with each one applying to a certain interval of the input variable. In problems like the commission calculation, different formulas are applied depending on whether sales are below or above a specific threshold.

Linear Equations

This concept pertains to equations of the first degree, where solving for an unknown variable involves isolating it using algebraic operations. In these scenarios, once the correct sub-function from the piecewise definition is chosen, setting up and solving such an equation leads to the determination of the unknown quantity.

Case Analysis

This involves breaking down a problem into separate cases based on different conditions or intervals of the input variable. By analyzing each case individually, one can determine which scenario is applicable and derive the correct equation to solve the problem.

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