Question

Liz earns a salary of $2,000 per month, plus a commission of 3% of her sales. She wants to earn at least $2,700 this month. Enter an inequality to find amounts of sales that will meet her goal. Identify what your variable represents. Enter the commission rate as a decimal.

Answer 1

She wants to earn a salary that is $2,700 or more, so we can write this as:

$S(x)\ge2700$

Her salary S(x) depends on x, the amount of sales she makes.

If she sells $100 she will have a comission of 3%, what means a 0.03*100 = $3 addition to her salary.

This can be generalized as 0.03*x for the commissions.

Then, she had her salary composed by a fixed salary ($2,000) and a variable salary (0.03*x).

Then we can write S(x) as:

$S(x)=2000+0.03x$

Joining with the inequality above, we would have:

$2000+0.03x\ge2700$

We can solve this inequality for the amount of sales x as:

$\begin{gathered} 2000+0.03x\ge2700 \\ 0.03x\ge2700-2000 \\ 0.03x\ge700 \\ x\ge\frac{700}{0.03} \\ x\ge23333.34 \end{gathered}$

Answer:

The inequality to start solving the problem is 2000+0.03x>=2700.

The variable x represents the amount of sales she makes.

The value 0.03 is the commission rate in decimals.

The amount of sales she has to make to earn at least $2,700 is $23,333.34.