Question

GIVE OUT BRAINLY 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:

Answer 1

a) $\ 560+0.08x \geq \ 700$

b) $1750

c) See attachment

Step-by-step explanation:

a)

In order to solve the problem, we call

x = total amount of the sale

From the text we know that:

Kathleen earns a fixed salary of $560 per week, plus 8% commission on sales. Therefore we can write the amount earned by Kathleen as

$S=\ 560+0.08x$

where

x is the sale

0.08x represents the 8% of the sales.

We also know that she wants to earn at least $700, therefore the total amount earned by Kathleen (S) must be at least equal to 700$.

This means that the inequality to write is:

$S\geq \ 700$

which means

$\ 560+0.08x \geq \ 700$

b)

The inequality to solve is

$\ 560+0.08x \geq \ 700$

To solve it, we proceed as follows:

1) First, we subtract 560 from both sides, and we get:

$560+0.08x-560 \geq 700-560\\0.08x\geq 140$

2) Then, we divide both sides by 0.08, and we get:

$\frac{0.08x}{0.08}\geq \frac{140}[0.08}\\x\geq \ 1750$

Therefore, she needs to sell 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 picture.

On a graph, we represents an inequality as follows:

- We plot a dot at the value corresponding to the value where the inequality becomes an equality: so in this case, x = 1750

- The dot will be empty if the inequality has the sign > or <, while the dot will be full if the inequality has $\geq$ or $\leq$ ; so in this case, we have a full dot.

- Finally, we draw an arrow into the direction of the solutions of the inequality. In this case, the solution is "for numbers larger than 1750", and so we draw an arrow pointing to the right.