A salesperson’s total earnings consist of a base salary of x dollars per year, plus commission earnings of 11 %

Question

A salesperson&rsquo;s total earnings consist of a base salary of x dollars per year, plus commission earnings of 11 % of the total sales the salesperson makes during the year. This year, the salesperson has a goal for the total earnings to be at least 3 times and at most 4 times the base salary. Which of the following inequalities represents all possible values of total sales s , in dollars, the salesperson can make this year in order to meet that goal?

Accepted Answer

Choice B is correct. It&rsquo;s given that a salesperson's total earnings consist of a base salary of x dollars per year plus commission earnings of 11 % of the total sales the salesperson makes during the year. If the salesperson makes s dollars in total sales this year, the salesperson&rsquo;s total earnings can be represented by the expression x + 0.11 s . It&rsquo;s also given that the salesperson has a goal for the total earnings to be at least 3 times and at most 4 times the base salary, which can be represented by the expressions 3 x and 4 x , respectively. Therefore, this situation can be represented by the inequality 3 x &#8804; x + 0.11 s &#8804; 4 x . Subtracting x from each part of this inequality yields 2 x &#8804; 0.11 s &#8804; 3 x . Dividing each part of this inequality by 0.11 yields 2 0.11 x &#8804; s &#8804; 3 0.11 x . Therefore, the inequality 2 0.11 x &#8804; s &#8804; 3 0.11 x represents all possible values of total sales s , in dollars, the salesperson can make this year in order to meet their goal. Choice A is incorrect. This inequality represents a situation in which the total sales, rather than the total earnings, are at least 2 times and at most 3 times, rather than at least 3 times and at most 4 times, the base salary. Choice C is incorrect. This inequality represents a situation in which the total sales, rather than the total earnings, are at least 3 times and at most 4 times the base salary. Choice D is incorrect. This inequality represents a situation in which the total earnings are at least 4 times and at most 5 times, rather than at least 3 times and at most 4 times, the base salary.

Question a-sale