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 5 5 2 2 10 10 3
To justify the expense of the membership fee, Joyce would need to visit the zoo enough times that the total cost of paying $45 each time would exceed the cost of joining the membership and paying $20 each visit.
Let's calculate the total cost of paying $45 each time and the total cost of joining the membership and paying $20 each visit:
Total cost of paying $45 each time:
$45 x Number of visits
Total cost of joining the membership and paying $20 each visit:
$50 (membership fee) + $20 x Number of visits
To find the number of visits that would justify the membership fee, we need to set up an inequality:
$45 x Number of visits > $50 + $20 x Number of visits
Simplifying the equation, we have:
$25 x Number of visits > $50
Number of visits > $50 / $25
Number of visits > 2
Therefore, Joyce would need to visit the zoo at least 3 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 need to compare the total cost of paying $45 per visit versus joining the membership and paying $20 per visit.
Without the membership, the cost per visit is $45. With the membership, the cost per visit is $20, but there is also an additional one-time fee of $50.
Let's calculate the number of visits required for this membership to be justified:
1. Total cost without the membership:
Cost per visit: $45
Number of visits required to justify the membership fee: ???
2. Total cost with the membership:
Cost per visit: $20
Membership fee: $50
Number of visits required to justify the membership fee: ???
To find the number of visits required to justify the membership fee, we can set up an equation:
Total cost without the membership = Total cost with the membership
45 * Number of visits required to justify the membership fee = 20 * Number of visits required to justify the membership fee + 50
Simplifying the equation:
45N = 20N + 50
25N = 50
N = 50 / 25
N = 2
Therefore, Joyce will need to visit the zoo 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 need to compare the total cost of buying individual tickets each time versus the cost of purchasing a membership.
First, let's calculate the total cost of buying individual tickets. Each time Joyce visits the zoo, she needs to pay $45.
Now, let's calculate the cost of purchasing a membership plus the reduced ticket prices. The membership fee is $50, and after that, each visit only costs $20.
To find the breakeven point, we need to calculate how many times Joyce would need to visit the zoo for the total cost of individual tickets to be equivalent to the cost of purchasing a membership plus the reduced ticket prices.
Let's go through the calculations:
1. Total cost of individual tickets: $45 x 5 visits = $225
2. Cost of purchasing a membership plus reduced ticket prices: $50 (membership fee) + $20 x 5 visits = $50 + $100 = $150
Based on these calculations, Joyce would need to visit the zoo at least 5 times to justify the expense of the membership fee.
Therefore, the correct answer is "5".