A salesperson earns $200 a week plus a 4% commission on her sales. Which equation models the relationship between her sales in a given week, $s$, and her weekly earnings, $e$?
A. [tex]e=\frac{200 s+4}{100}[/tex]
B. [tex]e=200 s+4[/tex]
C. [tex]e=4 s+200[/tex]
D. [tex]e=\frac{4}{100} s+200[/tex]
Answer (2)
The salesperson's weekly earnings consist of a fixed salary and a commission on sales. The commission is 4% of the sales, s , which is 100 4 s . The total earnings, e , is the sum of the fixed salary and the commission, so e = 100 4 s + 200 . The equation that models the relationship between sales and weekly earnings is e = 100 4 s + 200 .
Explanation
Problem Analysis Let's analyze the problem. The salesperson has a base salary and earns a commission based on sales. We need to formulate an equation that represents the total earnings.
Fixed Salary The salesperson earns a fixed salary of $200 per week.
Commission Calculation The salesperson earns a commission of 4% on her sales, s . This can be written as 0.04 s or 100 4 s .
Total Earnings Equation The total weekly earnings, e , is the sum of the fixed salary and the commission. Therefore, e = 200 + 100 4 s .
Final Equation We can rewrite the equation as e = 100 4 s + 200 . Comparing this with the given options, we find that it matches the fourth option.
Examples
Understanding how earnings are calculated based on a base salary plus commission is crucial in many sales jobs. For example, if a car salesperson earns a base salary of $500 per week and a 2% commission on sales, we can use this equation to determine their weekly earnings. If they sell 50 , 000 w or t h o f c a rs ina w ee k , t h e i re a r nin g s w o u l d b e e = 500 + 0.02(50000) = 500 + 1000 = $1500. This helps both the salesperson and the employer understand the earning potential and budget accordingly.
The equation that models the relationship between the salesperson's sales s and her weekly earnings e is e = 100 4 s + 200 , corresponding to option D. This equation includes a fixed salary of $200 plus a commission of 4% on sales. Therefore, the correct answer is D.
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