Question
Patty sells custom T-shirts on Etsy. She spent $504 on screen-printing tools and each shirt costs her $4.50 in supplies to create. She sells the shirts for $15 each.
Part 1:
Which equation can you use to find s, the number of T-shirts Patty must sell for her sales to equal her expenses?
Responses
4.5s + 15s = 504
4.5s + 15s = 504
15s = 504 + 4.5s
15s = 504 + 4.5s
504 + 15s = 4.5s
504 + 15s = 4.5s
504 - 4.5s = 15s
504 - 4.5s = 15s
Question 2
Part 2:
How many T-shirts must Patty sell for her sales to equal her expenses?
T-shirts
Part 1:
Which equation can you use to find s, the number of T-shirts Patty must sell for her sales to equal her expenses?
Responses
4.5s + 15s = 504
4.5s + 15s = 504
15s = 504 + 4.5s
15s = 504 + 4.5s
504 + 15s = 4.5s
504 + 15s = 4.5s
504 - 4.5s = 15s
504 - 4.5s = 15s
Question 2
Part 2:
How many T-shirts must Patty sell for her sales to equal her expenses?
T-shirts
Answers
GPT-4o mini
To find the number of T-shirts Patty must sell for her sales to equal her expenses, we first need to identify Patty's expenses and revenues.
**Expenses:**
- Initial investment in screen-printing tools: $504
- Cost per T-shirt: $4.50
If Patty sells \(s\) T-shirts, her total costs (expenses) will be:
\[
\text{Total Costs} = 504 + 4.50s
\]
**Revenues:**
- Selling price per T-shirt: $15
If Patty sells \(s\) T-shirts, her total revenue will be:
\[
\text{Total Revenue} = 15s
\]
To find out when her sales equal her expenses, we set the total revenues equal to total expenses:
\[
15s = 504 + 4.5s
\]
So the correct equation to use is:
\[
15s = 504 + 4.5s
\]
Now, let's solve for \(s\).
1. Subtract \(4.5s\) from both sides:
\[
15s - 4.5s = 504
\]
\[
10.5s = 504
\]
2. Divide both sides by 10.5:
\[
s = \frac{504}{10.5}
\]
\[
s = 48
\]
**Part 2: How many T-shirts must Patty sell for her sales to equal her expenses?**
Patty must sell **48 T-shirts**.
**Expenses:**
- Initial investment in screen-printing tools: $504
- Cost per T-shirt: $4.50
If Patty sells \(s\) T-shirts, her total costs (expenses) will be:
\[
\text{Total Costs} = 504 + 4.50s
\]
**Revenues:**
- Selling price per T-shirt: $15
If Patty sells \(s\) T-shirts, her total revenue will be:
\[
\text{Total Revenue} = 15s
\]
To find out when her sales equal her expenses, we set the total revenues equal to total expenses:
\[
15s = 504 + 4.5s
\]
So the correct equation to use is:
\[
15s = 504 + 4.5s
\]
Now, let's solve for \(s\).
1. Subtract \(4.5s\) from both sides:
\[
15s - 4.5s = 504
\]
\[
10.5s = 504
\]
2. Divide both sides by 10.5:
\[
s = \frac{504}{10.5}
\]
\[
s = 48
\]
**Part 2: How many T-shirts must Patty sell for her sales to equal her expenses?**
Patty must sell **48 T-shirts**.