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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) O 10 5 3 2
To determine the number of times Joyce will need to visit the zoo to justify the expense of the membership fee, we need to compare the total cost of visiting the zoo without a membership to the cost of visiting the zoo with a membership.
Without a membership:
Cost per visit = $45
Total cost for x visits = $45 * x
With a membership:
Membership fee = $50
Cost per visit = $20
Total cost for x visits = $50 + $20 * x
We can set up an equation to find the number of visits:
$45 * x = $50 + $20 * x
Now, we can solve for x:
$45x - $20x = $50
$25x = $50
x = $50/$25
x = 2
Therefore, Joyce will need to visit the zoo at least 2 times to justify the expense of the membership fee.
To justify the expense of the membership fee, Joyce needs to visit the zoo enough times that the total cost of individual visits becomes higher than the cost of the membership plus discounted visits.
Let's calculate the cost of individual visits: $45 each.
To calculate the cost of the membership plus discounted visits, we first need to subtract the discounted visit cost from the membership fee:
Membership fee: $50
Cost per visit with membership: $20
$50 - $20 = $30
Now we can divide the membership fee by the cost difference per visit:
$30 / ($45 - $20) = $30 / $25 = 1.2.
To make sense of the result, we must round it up since Joyce cannot visit the zoo a fraction of a time. Thus, Joyce would need to visit the zoo at least 2 times to justify the expense of the membership fee.
To find out how many times Joyce needs to visit the zoo to justify the expense of the membership fee, we need to compare the total cost of visiting the zoo without a membership to the total cost of visiting the zoo with a membership.
Without a membership, Joyce would pay $45 each time she visits the zoo.
With a membership, Joyce would pay an initial fee of $50 for the membership and $20 for each visit.
So, let's calculate the total cost of visiting the zoo without a membership and with a membership for different numbers of visits:
1. Without a membership: $45 per visit.
2. With a membership: $50 (membership fee) + $20 (per visit).
For each scenario, let's calculate the total cost:
1. Without a membership:
Total Cost = $45 x 1 = $45
2. With a membership:
Total Cost = $50 (membership fee) + $20 x 1 = $70
Comparing the two scenarios, we see that with only one visit, it is more expensive to have a membership ($70) compared to not having a membership ($45).
Similarly, let's calculate the total cost for more visits:
1. Without a membership:
Total Cost = $45 x 2 = $90
2. With a membership:
Total Cost = $50 (membership fee) + $20 x 2 = $90
For two visits, both scenarios have the same total cost.
Next, let's calculate for three visits:
1. Without a membership:
Total Cost = $45 x 3 = $135
2. With a membership:
Total Cost = $50 (membership fee) + $20 x 3 = $110
For three visits, it is cheaper to have a membership ($110) compared to not having a membership ($135).
Therefore, Joyce needs to visit the zoo at least 3 times to justify the expense of the membership fee.