Question

You work as a sales representative. You earn $\$400$ per week plus $5\%$ of your total sales for the week.

Part A: Last week, you had total sales of $\$5000$. Find your total earnings. Show your work.

Part B: One week, you earned $\$1350$. Let s represent your total sales that week. Write an equation that you can use to find s.

Part C: Using your equation from Part B, find s. Show all steps clearly.

Answer 1

Step1- Part A:

Let $x$represent the total income of the week and let $t$ represent total trade for the week.

Total income is the sum of pay per week, $\$400$ and $5\%$ of total trade for the week:

$x=400+5\%·t$

Insert the total trade for the week $t=5000$ into the equation:

$x=400+5\%·5000$

Solve the equation:

$x=400+5\%\times 5000$

Solving for $x$ we get,

$$\begin{gathered} x=400+\frac{5}{100}\times 5000 \\ x=400+5\times 50 \\ x=400+250 \\ x=650 \end{gathered}$$

Total income is $\$650$.

Step2- Part B:

Let A be the total earnings for a week.

The total earnings consist of the base salary of $\$400$ plus $5\%=0.05$ of the total sales S:

$A=\$400+0.05S$

Substituting $A=\$1350$ into the equation:

$\$1350=\$400+0.05S$

The equation that can be used to find the total sales S is:

$\$1350=\$400+0.05S$

Step3- Part C:

Equation from the previous part is:

$\$1350=\$400+0.05S$

Subtract $400$ from both sides of the equation:

$$\begin{gathered} 1350-400=400+0.05S-400 \\ 950=0.05s \end{gathered}$$

Divide both side of the equation by $0.05$, We get

$s=19000$

The total amount of sold items was $\$19,000.$