Question

A salesperson makes a base salary of $2100 per month. Once he reaches $42,000 in total sales, he earns an additional 5% commission on the amount in sales over $42,000.

(1) Graph the function.
(2) If the salesperson had $80,000 in sales, how much was his salary?
(3) If the salesperson's total salary for a month was $4500, how much were his total sales for that month?
(4) Compute S(25000) and interpret what this means in the context of the problem.

Answer 1

(1) Observe the attached image

(2)
`S = \$4,000`

(3)
`x = \$90,000`

(4)
`S = 2100`

Explanation:

(1) Let's call S the salary for the month the seller wins.

Let's call x the amount of dollars reached by the sales of that month.

The seller earns a base salary of $ 2100 per month.

Then, if x> 42,000 he wins a commission of 5% on sales.

Then the equation modeling this situation is:

`S =\left\{{{0.05(x-42,000)+2100\ if\ x>42,000} \atop{2,100\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ if\ 0\leq x\leq42,000}}\right.`

The graph of the function is shown in the attached image.

(2) If x = 80,000, then your salary was:

`S = 0.05(80000-42000) +2100\\\\S = \$4,000`

(3) If S was 4500 and we want to find x then we equal S to 4500 and solve for x.

`S = 4,500 = 0.05(x-42,000) + 2,100\\\\(2,400)/(0.05) = (x-42,000)\\\\x = (2400)/(0.05) +42,000\\\\x = \$90,000`

(4) S (25000) means that x equals 25000. Since x represents sales, this means that during the month, the seller only reached $ 25,000.

Then
`x <42000`

Therefore
`S = 2100`.