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

2
2

3
3

5

Answer 1

To find out how many times Joyce needs to visit the zoo to justify the membership fee, we can set up the costs for both options and find the point where they break even.

1. Single Visit Cost: $45 per visit

   • If Joyce visits the zoo \( x \) times, the cost will be:
     \[ \text{Cost without membership} = 45x \]

2. Membership Cost: $50 for the membership plus $20 per visit

   • If Joyce visits the zoo \( x \) times, the cost will be:
     \[ \text{Cost with membership} = 50 + 20x \]

To find the break-even point, we set the two costs equal to each other: \[ 45x = 50 + 20x \]

Now, subtract \( 20x \) from both sides: \[ 45x - 20x = 50 \] \[ 25x = 50 \]

Next, divide both sides by 25: \[ x = 2 \]

So, Joyce needs to visit the zoo 2 times to justify the expense of the membership fee.

The answer is 2.