joyce wants to go the the zoo with her friends over summer 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 expensive 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 visiting without a membership is equal to or greater than the cost with a membership.
Let's calculate the cost of visiting the zoo without a membership:
Visits without a membership: 45$ per visit
Total cost without a membership: 45$ * the number of visits
Now let's calculate the cost of getting a membership and visiting the zoo:
Membership fee: 50$
Price per visit with a membership: 20$
Visits with a membership: the number of visits
To find the number of visits needed to justify the expense of the membership fee, we need to set up the following equation:
Total cost without a membership = Membership fee + (Price per visit with a membership * the number of visits)
45$ * the number of visits = 50$ + (20$ * the number of visits)
Rearranging the equation, we get:
45$ * the number of visits - 20$ * the number of visits = 50$
Simplifying, we have:
25$ * the number of visits = 50$
Dividing both sides of the equation by 25$, we find:
the number of visits = 50$ / 25$
Therefore, Joyce needs 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, we can calculate the break-even point.
Let's assume x represents the number of times Joyce needs to visit the zoo.
If Joyce chooses to pay the admission fee each time, she would spend $45 per visit.
So, the total expense without a membership would be: Total expense without membership = 45 * x = 45x.
If Joyce chooses to purchase a membership, she would spend $50 for the membership fee and $20 per visit.
So, the total expense with a membership would be: Total expense with membership = 50 + 20 * x = 50 + 20x.
To find the point where the expenses are equal, we can set the two total expenses equal to each other and solve for x:
45x = 50 + 20x.
Subtracting 20x from both sides gives:
25x = 50.
Dividing both sides by 25 gives:
x = 2.
Therefore, Joyce would need to visit the zoo at least 2 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 need to compare the total cost of paying the individual entry fees with the total cost of purchasing the membership and paying the discounted price for each visit.
Let's analyze the costs:
Option 1: Paying individual entry fees
Cost per visit: $45
Option 2: Purchasing a membership
Membership fee: $50
Cost per visit with membership: $20
Now, we can calculate the number of visits necessary to justify the membership expense:
Total cost of individual visits = Number of visits × Cost per visit
Total cost of membership visits = Membership fee + (Number of visits × Discounted cost per visit)
To find the number of visits that makes the membership worthwhile, we can set the two costs equal to each other and solve for the unknown, which is the number of visits:
Number of visits × $45 = $50 + (Number of visits × $20)
Now, let's solve the equation:
Number of visits × $45 = $50 + Number of visits × $20
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 will need to visit the zoo at least 2 times to justify the expense of the membership fee.