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, 3, 5, 10
To justify the expense of the membership fee, Joyce would need to visit the zoo enough times so that the total cost of individual admissions exceeds the cost of a membership.
If Joyce chooses to pay $45 each time, she will spend $45 x n, where n is the number of visits.
If she chooses to get a membership, she will spend $50 for the membership fee plus $20 x n for the visits.
To find the break-even point, we can set the two expressions equal to each other and solve for n:
$45n = $50 + $20n
Subtracting $20n from both sides:
$45n - $20n = $50
Combining like terms:
$25n = $50
Dividing both sides by $25:
n = 2
Therefore, Joyce will need to visit the zoo at least 2 times to justify the expense of the membership fee.
To find out how many times Joyce would need to visit the zoo to justify the expense of the membership fee, we can compare the costs of the two options.
Option 1: Paying without membership
Joyce would have to pay $45 each time she visits the zoo.
Option 2: Paying with membership
Joyce would have to pay a membership fee of $50 upfront and then $20 for each visit to the zoo.
Let's calculate the costs for Joyce for different numbers of visits using the two options:
For 1 visit:
Option 1 cost: $45
Option 2 cost: $50 (membership fee) + $20 = $70
For 2 visits:
Option 1 cost: $45 x 2 = $90
Option 2 cost: $50 (membership fee) + $20 x 2 = $90
For 3 visits:
Option 1 cost: $45 x 3 = $135
Option 2 cost: $50 (membership fee) + $20 x 3 = $110
For 4 visits:
Option 1 cost: $45 x 4 = $180
Option 2 cost: $50 (membership fee) + $20 x 4 = $130
From the above calculations, we can see that after 3 visits, the cost of the membership option becomes less than the cost of paying without membership. Therefore, Joyce would need to visit the zoo at least 3 times to justify the expense of the membership fee.
So, the correct answer is 3 times.
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 visiting the zoo without a membership to the total cost with a membership.
Without a membership:
Total cost per visit = $45
So, the total cost of visiting the zoo without a membership will be 45n, where n is the number of visits.
With a membership:
Membership fee = $50
Cost per visit = $20
So, the total cost of visiting the zoo with a membership will be 50 + 20n.
To justify the expense of the membership fee, the total cost of visiting the zoo without a membership must be higher than the total cost of visiting the zoo with a membership.
So, we can set up the inequality: 45n > 50 + 20n.
Simplifying the inequality, we get: 25n > 50
Dividing both sides by 25, we get: n > 2
Therefore, Joyce will need to visit the zoo more than 2 times to justify the expense of the membership fee.
The correct answer is: 3