GIVE OUT 2) Kathleen is a sales associate in a jewelry store. She earns $560/wk plus an 8% commission on sales. How much does she need to sell in a week to earn at least $700 that week?

a. Write an inequality equation to solve the problem. Use your choice of variable.

b. How much does she need to sell to earn at least $700 that week?

c. Graph the solution on a number line.

Answers:

a)

b) $1750

c) See attachment

Step-by-step explanation:

a)

To solve the problem, we call:

= 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

where

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:

b)

The inequality that we have to solve is

First, we rewrite the  fraction as a number:

Then, we subtract 560 from both sides, and we get:

Finally, we divide both sides by 0.08, and we get:

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 or ; 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.

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