Question
Beth is buying coffee for everyone in her study group. If she goes to the café next to her school, it will cost her $3.25 per coffee. If she goes to the café by her home, it will cost her $3.75 per coffee, but she has a coupon for $5 off.
How many coffees would Beth need to buy for the two options to cost the same?
coffees
How many coffees would Beth need to buy for the two options to cost the same?
coffees
Answers
GPT-4o mini
Let \( n \) represent the number of coffees Beth buys.
1. **Cost at the café next to her school**:
\[
\text{Cost} = 3.25n
\]
2. **Cost at the café by her home**:
\[
\text{Cost} = 3.75n - 5
\]
To find the number of coffees where both options cost the same, we set the two costs equal to each other:
\[
3.25n = 3.75n - 5
\]
Now, we will solve this equation for \( n \).
First, isolate the terms involving \( n \) by subtracting \( 3.25n \) from both sides:
\[
0 = 3.75n - 3.25n - 5
\]
Simplifying the left-hand side gives:
\[
0 = 0.5n - 5
\]
Next, add 5 to both sides:
\[
5 = 0.5n
\]
Now, solve for \( n \) by multiplying both sides by 2:
\[
n = 10
\]
Thus, Beth would need to buy \(\boxed{10}\) coffees for the two options to cost the same.
1. **Cost at the café next to her school**:
\[
\text{Cost} = 3.25n
\]
2. **Cost at the café by her home**:
\[
\text{Cost} = 3.75n - 5
\]
To find the number of coffees where both options cost the same, we set the two costs equal to each other:
\[
3.25n = 3.75n - 5
\]
Now, we will solve this equation for \( n \).
First, isolate the terms involving \( n \) by subtracting \( 3.25n \) from both sides:
\[
0 = 3.75n - 3.25n - 5
\]
Simplifying the left-hand side gives:
\[
0 = 0.5n - 5
\]
Next, add 5 to both sides:
\[
5 = 0.5n
\]
Now, solve for \( n \) by multiplying both sides by 2:
\[
n = 10
\]
Thus, Beth would need to buy \(\boxed{10}\) coffees for the two options to cost the same.