Question

Kayla has a weekly budget of $880. She works at a clothing store and makes $315 per week, plus 20% commission on the merchandise she sells to her customers. The graph below models the dollar amount of merchandise Kayla sells each week.


2800280528102815282028252830283528402845285028552860

Which of the following is the correct interpretation of the solution?

A.
Kayla can sell less than $2,825 to reach her weekly budget.
B.
Kayla needs to sell $2,825 or more to reach her weekly budget.
C.
Kayla can sell $2,825 or less to reach her weekly budget.
D.
Kayla needs to sell more than $2,825 to reach her weekly budget.

Answer 1

To determine the correct interpretation of the solution regarding Kayla's commission and budget, we can analyze her income based on her selling performance.

1. Kayla's weekly income is composed of a fixed salary plus commission:
- Fixed salary = $315
- Commission = 20% of the merchandise sold.

2. To reach her weekly budget of $880, we can express her total income as:
\[
\text{Total Income} = 315 + 0.20 \times \text{Merchandise Sold}
\]

3. Setting this equal to her budget:
\[
315 + 0.20 \times \text{Merchandise Sold} \geq 880
\]

4. We can solve for the amount of merchandise Kayla needs to sell:
\[
0.20 \times \text{Merchandise Sold} \geq 880 - 315
\]
\[
0.20 \times \text{Merchandise Sold} \geq 565
\]
\[
\text{Merchandise Sold} \geq \frac{565}{0.20} = 2825
\]

This calculation shows that Kayla needs to sell **at least $2,825** in merchandise to reach her weekly budget of $880.

Thus, the correct interpretation of the solution is:
**B. Kayla needs to sell $2,825 or more to reach her weekly budget.**