Catherine makes a base salary of $400 per week plus 12% commission on the amount

Question

Catherine makes a base salary of $400 per week plus 12% commission on the amount of money she makes from her sales. Write a linear function to model Catherine's weekly salary, S (x). Indicate what the variable x represents, and make sure to utilize function notation. Evaluate S (8000). Write a complete sentence that interprets the meaning of S (8000) in the context this problem. If Catherine's weekly paycheck was $2000, how many salts did she make? If Catherine's friend Jorge makes $300 per week plus 14% commission, how many sales musts they make in order to have the same weekly paycheck? For what range of sales will Catherine's paycheck always be greater than Jorge's paycheck? Write your answer using interval notation. Graph the equations representing both Catherine's and Jorge's weekly paychecks on the same coordinate system. Use a straight edge and clearly indicate the intersection point and all intercepts.

Explanation / Answer

a) S(x) = 400 + 0.12x

x is the amount she makes from sales

b) S(8000) = 400 + 0.12*8000 = $ 1360

c) S(8000) is the amount of salary based on sales of $ 8000

d) S(x) = $ 2000 ; solve for x

2000 = 400 + 0.12x ; x = $ 13333.33 sales

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