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

Question

whpalmer4 · Answer

Kathleen's earnings are $560+8\%*\text{sales}$

Set that equal to $700$ and solve for the amount of sales.

hellomynameiskam · Answer

im confused @whpalmer4

mathstudent55 · Answer

Kathleen earns $560 per week plus an amount that depends on her sales.
Let's say Kathleen sells x amount of dollars in a week.
The commission she will earn on the sales is 8% of x.
Since 8% = 0.08, then 8% of x is 0.08x
That means that for that week, she will earn 560 + 0.08x.
Ok so far?

hellomynameiskam · Answer

yes.

hellomynameiskam · Answer

560 + 0.08x = 560.08
thats what i got

mathstudent55 · Answer

No.
She wants to earn 700, so we need to use 700.
Also, she wants to earn at least $700.
That means this problem needs an inequality.

mathstudent55 · Answer

Since she wants to earn at least $700, that means the amount she earns must be greater than or equal to 700.
She will earn 560 + 0.08x
We want that amount to be greater than or equal to 700, so we setup an inequality:

$560 + 0.08x \ge 700$

mathstudent55 · Answer

The inequality above uses the unknown amount in sales, x, that she needs to sell to earn at least $700 in that week.
Now you need to solve the inequality for x to find how much she needs to sell in that week.

whpalmer4 · Answer

It's a fine point, but the amount she NEEDS to sell to earn at least $700 is given by $$700 = 560 + 0.08x$$Any sales beyond that value of $x$ simply pad her income.  There is only one value of $x$ which is the minimum amount of sales she can make to earn $700 for the week.  "How much does she need to sell" -> "What is the minimum value of sales"