Question

Nataly is considering two job offers. The first job would pay her $\backslash (83,000$per year. The second would pay her $\backslash )66,500$plus $15\%$of her total sales. What would her total sales need to be for her salary on the second offer be higher than the first?

Short answer

Nataly total sales need to be for her salary on the second offer be higher than the first is,$\$110,000$.

Step-by-step solution

Step 1. Given information

The pay for the first job is,$\$83,000$.

The pay for the second job is,$\$66,500$.

The given percent of the total sales is,$15\%$.

Let the required total sales be,$\$x$.

It is also mentioned that, Nataly's salary on the second offer be higher than the first.

From the given information, let us create an equation.

$66,500+\left(15\%\right)x\ge 83,000$

Step 2. Now simplify the obtained equation.

$$\begin{gathered} 66,500+\left(15\%\right)x\ge 83,000 \\ \left(15\%\right)x\ge 83,000-66,500 \\ \left(\frac{15}{100}\right)x\ge 16,500 \\ \left(0.15\right)x\ge 16,500 \\ x\ge \frac{16500}{0.15} \\ x\ge 110,000 \end{gathered}$$

Step 3. Let us check the answer.

$$\begin{gathered} 66,500+\left(15\%\right)x\ge 83,000 \\ 66,500+\left(15\%\right)110,000\ge 83,000 \\ 66,500+\left(0.15\right)110,000\ge 83,000 \\ 66,500+16,500\ge 83,000 \\ 83,000\ge 83,000 \end{gathered}$$

which is true.

Therefore, Nataly total sales need to be for her salary on the second offer be higher than the first is,$\$110,000$.