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
2
2
3
3
5
5
10
To justify the expense of the membership fee, Joyce would need to visit the zoo ___________ times.
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 paying the individual entry fee each time versus the cost of joining the membership and paying the discounted price per visit.
Without the membership:
Cost per visit: $45
Total cost for x visits: 45x
With the membership:
Membership fee: $50
Discounted price per visit: $20
Total cost for x visits: 50 + 20x
To find the number of visits needed to justify the expense of the membership fee, we can set up the following equation:
45x ≥ 50 + 20x
Subtracting 20x from both sides:
25x ≥ 50
Dividing by 25:
x ≥ 2
Therefore, Joyce will need to visit the zoo at least 2 times to justify the expense of the membership fee.
To determine the number of times Joyce needs to visit the zoo to justify the expense of the membership fee, let's analyze the cost options.
Without a membership:
- Joyce pays $45 per visit to the zoo.
With a membership:
- Joyce pays a $50 membership fee initially.
- After becoming a member, she pays only $20 per visit to the zoo.
To determine the breakeven point, we need to compare the total cost of visiting the zoo with and without the membership.
Without a membership, the total cost can be calculated by multiplying the cost per visit ($45) by the number of visits.
With a membership, the total cost can be calculated as the sum of the membership fee ($50) and the cost per visit ($20) multiplied by the number of visits.
Let's set up an equation to solve for the number of visits needed to justify the membership fee.
Cost without membership = Cost with membership
$45 * number of visits = $50 + ($20 * number of visits)
Now, let's solve the equation:
45 * number of visits = 50 + 20 * number of visits
45 * number of visits - 20 * number of visits = 50
25 * number of visits = 50
number of visits = 50 / 25
number of visits = 2
Therefore, Joyce needs to visit the zoo at least 2 times to justify the expense of the membership fee.