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 calculate how many times Joyce needs to visit the zoo to justify the expense of the membership fee, we need to find the point at which the cost of visiting the zoo without the membership exceeds the cost of getting the membership.
Cost of visiting the zoo without membership = $45 per visit
Cost of visiting the zoo with membership = $20 per visit (after paying the $50 membership fee)
Let's set up the equation:
$45 x x > $50 + ($20 x x)
Where x is the number of visits Joyce needs to make to justify the membership fee.
Simplifying the equation:
$45x > $50 + $20x
Subtracting $20x from both sides of the equation:
$45x - $20x > $50
Combining like terms:
$25x > $50
Dividing both sides of the equation by $25:
x > 2
Since Joyce cannot make a fraction of a visit, she needs to visit the zoo at least 3 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 visiting the zoo using both options.
Option 1: Paying $45 each time
Option 2: Paying $50 for a membership and $20 for each visit
Since the membership fee is a one-time expense, we can exclude it from the equation of total cost.
Let's start by comparing the cost of visiting the zoo 1 time using both options:
Option 1: $45
Option 2: $50 (membership fee) + $20 = $70
Visiting the zoo 1 time is cheaper in option 1.
Now, let's compare the cost of visiting the zoo 2 times using both options:
Option 1: 2 x $45 = $90
Option 2: $50 (membership fee) + 2 x $20 = $90
Visiting the zoo 2 times costs the same in both options.
Therefore, if Joyce plans on visiting the zoo at least 2 times, it would justify the expense of the membership fee. Any additional visits after that would result in cost savings.
In conclusion, 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 individually each time to the cost of purchasing a membership.
If Joyce pays individually each time without a membership, the cost per visit is $45.
If Joyce purchases a membership, she would need to pay the initial fee of $50 upfront, and then only pay $20 per visit.
To determine the breakeven point, we need to find when the total cost of paying individually each time equals the cost of purchasing a membership and then paying the reduced visit fee.
Let's set up an equation to represent this situation:
Total cost without membership = Total cost with membership
Let's call the number of visits needed to justify the membership fee "x".
For paying individually each time:
Total cost without membership = 45x
For purchasing a membership and then paying the reduced visit fee:
Total cost with membership = 50 + 20x
Now, we can set up an equation and solve for x:
45x = 50 + 20x
To isolate the variable x, we subtract 20x from both sides:
45x - 20x = 50
25x = 50
Divide both sides by 25:
x = 2
Therefore, Joyce would need to visit the zoo at least 2 times to justify the expense of the membership fee.