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)
To justify the expense of the membership fee, Joyce needs to visit the zoo enough times so that the total cost of individual visits is greater than the cost of the membership.
Let's calculate the total cost of individual visits:
Cost per individual visit = $45
So, the total cost of individual visits without the membership = $45 x number of visits
And let's calculate the total cost with the membership:
Membership cost = $50
Visit cost with the membership = $20
So, the total cost with the membership = Membership cost + (Visit cost with the membership x number of visits)
For the membership to be justified, the total cost without the membership should be greater than the total cost with the membership.
In other words, we need to solve the inequality:
$45 x number of visits > $50 + ($20 x number of visits)
$45 x number of visits - $20 x number of visits > $50
$25 x number of visits > $50
number of visits > $50 / $25
number of visits > 2
So, Joyce needs to visit the zoo more than 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 paying the regular admission fee each time with the total cost of having the membership.
First, let's calculate the total cost of paying the regular admission fee each time. Since Joyce will need to pay $45 for each visit, we can represent the total cost of visiting the zoo without a membership as:
Total Cost without Membership = $45 x Number of Visits
Now, let's calculate the total cost of having the membership. With the membership, Joyce will pay $50 upfront and then only $20 for each visit. The $50 is a one-time expense, but for each visit after that, she only pays $20. So we can represent the total cost of having the membership as:
Total Cost with Membership = $50 (Membership Fee) + $20 x Number of Visits
To determine when having the membership becomes more cost-effective, we need to find the point where the total cost with the membership is equal to or less than the total cost without the membership. In other words, we need to solve the following equation:
Total Cost without Membership = Total Cost with Membership
$45 x Number of Visits = $50 + $20 x Number of Visits
To solve for the number of visits, we can subtract $50 from both sides of the equation and then divide both sides by the difference in costs per visit (which is $45 - $20 = $25):
$45 x Number of Visits - $20 x Number of Visits = $50
$25 x Number of Visits = $50
Number of Visits = $50 / $25
Number of Visits = 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 will need to visit the zoo to justify the expense of the membership fee, let's compare the total cost of visiting the zoo without a membership to the total cost with a membership.
Without a membership:
Cost per visit = $45
Total cost without membership = Cost per visit * Number of visits
With a membership:
Membership fee = $50
Cost per visit with membership = $20
Total cost with membership = Membership fee + (Cost per visit with membership * Number of visits)
To find the number of visits that will justify the expense of the membership fee, we need to compare the total costs.
Total cost without membership = Total cost with membership
Cost per visit * Number of visits = Membership fee + (Cost per visit with membership * Number of visits)
Let's solve for the number of visits (x):
$45x = $50 + ($20x)
$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.