A salesperson is paid a base salary of $300 a week plus a 5% commission on the sales he generates. Which inequality best represents s, the amount of sales in dollars he must generate to earn more than $500 for the week? s greater-than 25 s greater-than 200 s greater-than 4,000 s greater-than 16,000

Step-by-Step:

A salesperson receives a base salary of $300 per week and a commission of 15% on all sales over $5,000. If x represents the salesperson’s weekly sales, express the total weekly earnings E(x) as a function of x and simplify the expression. Then find E(2,000) and E(7,000) and E(10,000).

15% as a decimal is written as 0.15.

Build our weekly earnings function

E(x) = Commission + Base Salary

E(x) = 0.15(Max(0, x - 5000)) + 300

Now find the sales salary for 2,000, 7,000, and 10,000 in sales

E(2,000) = 0.15(Max(0,2000 - 5000)) + 300

E(2,000) = 0.15(Max(0,-3000)) + 300

E(2,000) = 0.15(0) + 300

E(2,000) = 300

E(7,000) = 0.15(Max(0,7000 - 5000)) + 300

E(7,000) = 0.15(Max(0,2000)) + 300

E(7,000) = 0.15(2,000) + 300

E(7,000) = 300 + 300

E(7,000) = 600

E(10,000) = 0.15(Max(0,10000 - 5000)) + 300

E(10,000) = 0.15(Max(0,5000)) + 300

E(10,000) = 0.15(5,000) + 300

E(10,000) = 750+ 300

E(10,000) = 1,050