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)%0D%0AResponses%0D%0A%0D%0A3%0D%0A3%0D%0A%0D%0A2%0D%0A2%0D%0A%0D%0A5%0D%0A5%0D%0A%0D%0A10
To justify the expense of the membership fee, Joyce needs to visit the zoo enough times to make up for the cost difference between paying for each visit and having a membership.
The cost difference between paying for each visit and having a membership is $45 (cost of each visit) - $20 (cost per visit with membership) = $25.
To calculate how many times Joyce needs to visit the zoo to justify the expense of the membership fee, divide the cost of the membership fee by the cost difference: $50 (membership fee) / $25 (cost difference) = 2.
Therefore, Joyce needs to visit the zoo at least 2 times to justify the expense of the membership fee.
To determine how many times Joyce will need to visit the zoo to justify the expense of the membership fee, we can compare the total cost of visiting the zoo without the membership to the total cost with the membership.
Without the membership:
Cost per visit = $45
Total cost without membership = $45 * number of visits
With the membership:
Membership fee = $50
Cost per visit with membership = $20
Total cost with membership = $50 (membership fee) + $20 (cost per visit) * number of visits
We need to find the number of visits at which the total cost with the membership is equal to or lower than the total cost without the membership.
Setting up the equation:
$50 + $20 * number of visits ≤ $45 * number of visits
Simplifying the equation:
$50 ≤ $45 * number of visits - $20 * number of visits
$50 ≤ $25 * number of visits
Dividing both sides of the equation by 25:
$50/25 ≤ number of visits
Simplifying the inequality:
2 ≤ number of visits
Therefore, Joyce will need to visit the zoo at least 2 times to justify the expense of the membership fee.
To determine how many times Joyce needs to visit the zoo to justify the expense of the membership fee, we need to compare the costs of both options.
Option 1: Paying $45 each time to get into the zoo.
Option 2: Joining a membership for $50 and then paying $20 each visit to the zoo.
Let's first calculate how many visits Joyce would need to make under Option 1:
45x = y
Where:
x = number of visits
y = cost under Option 1
Now let's calculate the cost under Option 2:
50 + 20x = y
We can set these two equations equal to each other to find the break-even point:
45x = 50 + 20x
Subtracting 20x from both sides gives:
25x = 50
Dividing both sides by 25:
x = 2
So, Joyce would need to visit the zoo at least 2 times to justify the expense of the membership fee. Therefore, the correct answer is 2.