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?
Responses
5
2
10
3
To justify the expense of the membership fee, Joyce would need to visit the zoo 3 times.
Option 1: Without the membership
Cost per visit: $45
Total cost for 3 visits: 3 * $45 = $<<3*45=135>>
Option 2: With the membership
Membership fee: $50
Cost per visit: $20
Total cost for 3 visits: $50 + (3 * $20) = $50 + $60 = $<<50+60=110>>
Since $135 is greater than $110, 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 needs to visit the zoo to justify the expense of the membership fee, we can compare the costs without the membership to the costs with the membership.
Without membership:
Cost per visit = $45
Number of visits needed = ???
With membership:
Membership fee = $50
Cost per visit = $20
Number of visits needed = ???
Let's calculate the number of visits needed without membership first:
Cost per visit without membership = $45
Number of visits needed = $50 / $45 = 1.11 (rounded to the nearest whole number)
Since we cannot have a fraction of a visit, Joyce would need to visit the zoo at least 2 times without the membership to justify the expense of the membership fee.
Next, let's calculate the number of visits needed with the membership:
Membership fee = $50
Cost per visit with membership = $20
Number of visits needed = $50 / ($45 - $20) = $50 / $25 = 2
Therefore, Joyce would need to visit the zoo at least 3 times with the membership to justify the expense of the membership fee.
So the correct answer is 3.
To determine how many times Joyce will need to visit the zoo to justify the expense of the membership fee, let's compare the costs of the two options.
First, let's calculate the cost of visiting the zoo without the membership. Joyce would pay $45 each time.
Next, let's calculate the cost of getting the membership. Joyce would pay $50 upfront for the membership and then $20 for each visit to the zoo.
To find the break-even point, where the cost of the membership becomes more economical than paying without it, we need to set up an equation and solve for the number of visits.
The equation would be:
Number of visits * $20 (cost per visit with membership) = $50 (membership fee) + Number of visits * $45 (cost per visit without membership)
Let's simplify the equation:
20v = 50 + 45v
Where 'v' represents the number of visits.
Now, let's solve for 'v':
20v - 45v = 50
-25v = 50
v = -50 / -25
v = 2
Therefore, Joyce will need to visit the zoo at least 2 times to justify the expense of the membership fee.