Answer:
(1) Observe the attached image
(2) [tex]S = \$4,000[/tex]
(3) [tex]x = \$90,000[/tex]
(4) [tex]S = 2100[/tex]
Step-by-step 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:
[tex]S =\left\{{{0.05(x-42,000)+2100\ if\ x>42,000} \atop{2,100\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ if\ 0\leq x\leq42,000}}\right.[/tex]
The graph of the function is shown in the attached image.
(2) If x = 80,000, then your salary was:
[tex]S = 0.05(80000-42000) +2100\\\\S = \$4,000[/tex]
(3) If S was 4500 and we want to find x then we equal S to 4500 and solve for x.
[tex]S = 4,500 = 0.05(x-42,000) + 2,100\\\\\frac{2,400}{0.05} = (x-42,000)\\\\x = \frac{2400}{0.05} +42,000\\\\x = \$90,000[/tex]
(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 [tex]x <42000[/tex]
Therefore [tex]S = 2100[/tex].
