Question
Kayla has a weekly budget of $785. She works at a clothing store and makes $130 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.
3250325532603265327032753280328532903295330033053310
Which of the following is the correct interpretation of the solution?
A.
Kayla needs to sell $3,275 or more to reach her weekly budget.
B.
Kayla needs to sell more than $3,275 to reach her weekly budget.
C.
Kayla can sell less than $3,275 to reach her weekly budget.
D.
Kayla can sell $3,275 or less to reach her weekly budget.
3250325532603265327032753280328532903295330033053310
Which of the following is the correct interpretation of the solution?
A.
Kayla needs to sell $3,275 or more to reach her weekly budget.
B.
Kayla needs to sell more than $3,275 to reach her weekly budget.
C.
Kayla can sell less than $3,275 to reach her weekly budget.
D.
Kayla can sell $3,275 or less to reach her weekly budget.
Answers
GPT-4o mini
To determine the correct interpretation of the solution regarding Kayla's weekly budget and income, let's break down her earnings.
Kayla earns a fixed income of $130 per week plus 20% commission on the merchandise she sells.
Let's denote:
- The dollar amount of merchandise sold as \( x \).
- Her total income as \( I \).
Then the total income can be expressed as:
\[
I = 130 + 0.2x
\]
Her weekly budget is $785.
To find out how much merchandise she needs to sell to reach her budget, we set up the equation:
\[
130 + 0.2x = 785
\]
Now, we solve for \( x \):
1. Subtract 130 from both sides:
\[
0.2x = 785 - 130
\]
\[
0.2x = 655
\]
2. Divide both sides by 0.2:
\[
x = \frac{655}{0.2}
\]
\[
x = 3275
\]
This means Kayla needs to sell $3,275 in merchandise to exactly reach her weekly budget of $785.
Now, let's analyze the choices given:
- A. Kayla needs to sell $3,275 or more to reach her weekly budget. (This is true, she needs at least $3,275)
- B. Kayla needs to sell more than $3,275 to reach her weekly budget. (This is false, she can sell exactly $3,275)
- C. Kayla can sell less than $3,275 to reach her weekly budget. (This is false, selling less means she won't meet her budget)
- D. Kayla can sell $3,275 or less to reach her weekly budget. (This is false, she needs to sell at least $3,275)
The correct answer is:
**A. Kayla needs to sell $3,275 or more to reach her weekly budget.**
Kayla earns a fixed income of $130 per week plus 20% commission on the merchandise she sells.
Let's denote:
- The dollar amount of merchandise sold as \( x \).
- Her total income as \( I \).
Then the total income can be expressed as:
\[
I = 130 + 0.2x
\]
Her weekly budget is $785.
To find out how much merchandise she needs to sell to reach her budget, we set up the equation:
\[
130 + 0.2x = 785
\]
Now, we solve for \( x \):
1. Subtract 130 from both sides:
\[
0.2x = 785 - 130
\]
\[
0.2x = 655
\]
2. Divide both sides by 0.2:
\[
x = \frac{655}{0.2}
\]
\[
x = 3275
\]
This means Kayla needs to sell $3,275 in merchandise to exactly reach her weekly budget of $785.
Now, let's analyze the choices given:
- A. Kayla needs to sell $3,275 or more to reach her weekly budget. (This is true, she needs at least $3,275)
- B. Kayla needs to sell more than $3,275 to reach her weekly budget. (This is false, she can sell exactly $3,275)
- C. Kayla can sell less than $3,275 to reach her weekly budget. (This is false, selling less means she won't meet her budget)
- D. Kayla can sell $3,275 or less to reach her weekly budget. (This is false, she needs to sell at least $3,275)
The correct answer is:
**A. Kayla needs to sell $3,275 or more to reach her weekly budget.**