- The base salary is \(\$400\).
- The commission is \(10\%\) of sales \(s\), which is \(0.1s\).
- Total weekly earnings are the sum of the base salary and the commission: \(400 + 0.1s\).
- Thus, the expression represents Tasha's weekly earnings.
- Final Answer: \(\boxed{\text{Tasha's weekly earnings}}\)
Explanation
- Analysis of the Expression components
The problem asks us to identify the meaning of the expression \(400 + 0.1s\) based on Tasha's salary structure. We are given the following information:
- Tasha's fixed base salary each week is \(\$400\).
- She earns a commission of \(10\%\) on her total weekly sales, which are represented by the variable \(s\).
- The commission amount is calculated by taking \(10\%\) of her sales, which is written in decimal form as \(0.1 \times s = 0.1s\).
- Her total earnings for the week consist of her base salary plus the commission she earns from sales. Therefore, the total weekly earnings can be expressed as the sum of her base salary and her commission: \(400 + 0.1s\).
- Additionally, the problem notes she saves \(\frac{1}{4}\) of her earnings, but the expression \(400 + 0.1s\) itself only represents the total money earned, not the savings.
- Interpreting the expression
We have identified the two components of the expression \(400 + 0.1s\):
- The term \(400\) represents Tasha's fixed weekly base salary.
- The term \(0.1s\) represents the commission Tasha earns based on her sales \(s\).
Summing these two components, \(400 + 0.1s\), gives the total amount of money Tasha earns during a week before any deductions or savings. By comparing this to the options provided, we conclude that the expression \(400 + 0.1s\) represents Tasha's weekly earnings.
Examples
Understanding how to construct and interpret algebraic expressions is vital in personal finance and business management. For example, if you are planning a monthly budget, your total income might consist of a fixed salary plus a variable bonus based on your performance. Expressing this as an equation like \(I = B + rS\) (where \(I\) is income, \(B\) is base, \(r\) is rate, and \(S\) is sales) helps you calculate your total monthly earnings accurately and track how your performance influences your take-home pay.