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 justify the expense of the membership fee, Joyce needs to visit the zoo enough times such that the total cost of paying the entrance fee each time is greater than or equal to the cost of the membership fee.
Let's assume Joyce needs to visit the zoo x number of times.
If Joyce pays the entrance fee each time, she will spend 45x dollars.
If Joyce gets the membership, she will spend 50 + 20x dollars.
To justify the expense of the membership fee, 45x >= 50 + 20x.
By subtracting 20x from both sides of the equation, we get 25x >= 50.
By dividing both sides of the equation by 25, we get x >= 2.
Joyce needs to visit the zoo at least 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 individual visits with the cost of the membership plus the reduced rate for each visit.
Let's first consider the cost of individual visits:
- Joyce will pay $45 for each visit to the zoo without a membership.
Now let's consider the cost with a membership:
- Joyce will need to pay $50 for the membership fee.
- After getting the membership, each visit will cost $20.
To determine the break-even point, we need to find out how many visits Joyce would have to make for the total cost with a membership to be equal to or less than the total cost without a membership.
Let's denote the number of visits Joyce needs to make as "x".
Total cost without a membership = Cost per visit * Number of visits
Total cost without a membership = $45 * x
Total cost with a membership = Membership fee + (Cost per visit with membership * Number of visits)
Total cost with a membership = $50 + ($20 * x)
Now, we can set up the equation to find the break-even point:
$45 * x = $50 + ($20 * x)
To solve for "x", we can start by isolating the variable terms:
$45 * x - $20 * x = $50
Combining like terms:
$25 * x = $50
Now, solve for "x" by dividing both sides by $25:
x = $50 / $25
x = 2
Therefore, Joyce would need to visit the zoo at least 2 times for the membership to be justified.
To determine how many times Joyce will need to visit the zoo to justify the expense of the membership fee, we can set up an equation.
Let's assume Joyce visits the zoo x number of times.
If she pays the regular entrance fee each time, she will spend 45x dollars.
However, if she purchases the membership, she will pay an additional $50 upfront, and then only $20 per visit.
The total cost with a membership will be:
Membership fee + (Cost per visit * Number of visits)
= $50 + ($20 * x)
= $50 + $20x
Now, we need to find the number of visits x that would make the cost of purchasing the membership less than or equal to the cost of paying the regular entrance fee each time.
So, we need to solve the inequality:
$50 + $20x ≤ $45x
Simplifying the inequality:
$50 ≤ $45x - $20x
$50 ≤ $25x
Now, divide both sides of the inequality by $25:
$50 / $25 ≤ ($25x) / $25
2 ≤ x
Therefore, Joyce will need to visit the zoo at least 2 times to justify the expense of the membership fee.