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?
To determine how many times Joyce will need to visit the zoo to justify the expense of the membership fee, we can compare the total cost of paying for individual visits with the cost of purchasing a membership.
Option 1: Paying for individual visits
The cost of each visit is $45.
Option 2: Purchasing a membership
The membership fee is $50.
After purchasing the membership, each subsequent visit costs $20.
To find the breakeven point, we need to calculate how many visits Joyce would need to make for the total cost under each option to be equal.
Let's set up an equation to solve for the number of visits:
45x = 50 + 20x
Where:
x = the number of visits.
Simplifying the equation, we get:
45x = 50 + 20x
45x - 20x = 50
25x = 50
x = 50 / 25
x = 2
Joyce would 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 so that the total cost of paying $45 each time is greater than the total cost of joining the membership and paying $20 each time.
Let's assume Joyce will visit the zoo 'x' number of times.
The total cost of paying $45 each time is 45*x.
The total cost of joining the membership and paying $20 each time is the membership fee of $50 plus $20*x.
To justify the expense, we need to find the value of 'x' where 45*x > 50 + 20*x.
Subtracting 20*x from both sides of the equation, we get 45*x - 20*x > 50.
Combining like terms, 25*x > 50.
Dividing both sides by 25 gives us x > 2.
Therefore, Joyce needs to visit the zoo at least 3 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, we need to compare the total cost of paying $45 per visit to the total cost of paying $50 for the membership plus $20 per visit.
Let's assume Joyce will visit the zoo x number of times.
If Joyce pays $45 per visit, the total cost would be 45x dollars.
If Joyce chooses to join the membership, she will pay an additional $50 upfront. Then she will pay $20 for each visit. So the total cost would be 50 + 20x dollars.
To justify the expense of the membership fee, the total cost with the membership should be equal to or less than the cost without the membership.
Therefore, we can set up the following equation:
50 + 20x ≤ 45x
We can solve this equation to find the value of x:
50 ≤ 45x - 20x
50 ≤ 25x
50/25 ≤ x
2 ≤ x
So Joyce will need to visit the zoo at least 2 times to justify the expense of the membership fee.