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)

Question

Responses

10
10

5
5

2
2

3

Answer 1

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