a) [tex]560+\frac{8}{100}x>700[/tex]
b) $1750
c) See attachment
Step-by-step explanation:
a)
To solve the problem, we call:
[tex]x[/tex] = the total amount of the sale
We know that:
Kathleen earns a fixed salary of $560 per week, plus 8% commission on sales. So we can write the amount earned by Kathleen as
[tex]560+\frac{8}{100}x[/tex]
where
[tex]\frac{8}{100}x[/tex] represents the 8% of the sales.
We know that she wants to earn at least $700, so this total amount must be at least equal to 700$; so we can write the inequality:
[tex]560+\frac{8}{100}x\geq 700[/tex]
b)
The inequality that we have to solve is
[tex]560+\frac{8}{100}x\geq 700[/tex]
First, we rewrite the fraction as a number:
[tex]560+0.08x\geq 700[/tex]
Then, we subtract 560 from both sides, and we get:
[tex]560+0.08x-560\geq 700-560\\0.08x\geq 140[/tex]
Finally, we divide both sides by 0.08, and we get:
[tex]\frac{0.08x}{0.08}\geq \frac{140}{0.08}\\x\geq 1750[/tex]
So, she needs to seel at least $1750 that week, in order to earn at least $700.
c)
The solution graphed on a number line is shown in the attachment.
In order to represents an inequality:
- We draw a dot at the value where the inequality becomes an equality: in this case, at x = 1750
- The dot is empty if the inequality has > or <, while the dot is full if the inequality has [tex]\geq[/tex] or [tex]\leq[/tex]; so in this case, we will draw a full dot
- Then we draw an arrow going to the direction of the solutions of the inequality. In this case, the solution is "all numbers larger than 1750", so we draw an arrow to the right.
