Question
Joyce wants to go to the zoo with her friend over spring break. You can pay $45 to get into the zoo each time, or join a membership for $50 and then only pay $20 each visit to the zoo. How many times will Joyce need to visit the zoo to justify the expense of the membership fee?(1 point)
Responses
10
10
5
5
2
2
3
Responses
10
10
5
5
2
2
3
Answers
GPT-4o mini
To find out how many times Joyce needs to visit the zoo to justify the membership fee, we can set up the following equations:
- The cost of visiting the zoo without a membership for \( x \) visits: \( 45x \)
- The cost of visiting the zoo with a membership for \( x \) visits: \( 50 + 20x \)
We want to find the point at which these costs are equal:
\[ 45x = 50 + 20x \]
Now, let's solve for \( x \):
1. Subtract \( 20x \) from both sides:
\[ 45x - 20x = 50 \]
\[ 25x = 50 \]
2. Divide both sides by 25:
\[ x = \frac{50}{25} \]
\[ x = 2 \]
So, Joyce will need to visit the zoo **2 times** to justify the expense of the membership fee.
The correct response is:
**2**
- The cost of visiting the zoo without a membership for \( x \) visits: \( 45x \)
- The cost of visiting the zoo with a membership for \( x \) visits: \( 50 + 20x \)
We want to find the point at which these costs are equal:
\[ 45x = 50 + 20x \]
Now, let's solve for \( x \):
1. Subtract \( 20x \) from both sides:
\[ 45x - 20x = 50 \]
\[ 25x = 50 \]
2. Divide both sides by 25:
\[ x = \frac{50}{25} \]
\[ x = 2 \]
So, Joyce will need to visit the zoo **2 times** to justify the expense of the membership fee.
The correct response is:
**2**