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)
Responses
a 2
b 3
c 5
d 10
Let's calculate the cost of visiting the zoo without a membership. Joyce will pay $45 each time.
Now let's calculate the cost of visiting the zoo with a membership. Joyce will pay $50 for the membership fee and $20 each visit.
To justify the expense of the membership fee, Joyce needs to visit the zoo enough times so that the total cost with the membership is equal to or less than the total cost without the membership.
$50 + $20n ≤ $45n
Where n is the number of visits.
Simplifying the equation:
$20n - $45n ≤ -$50
-$25n ≤ -$50
To get rid of the negative sign, we will multiply both sides of the inequality by -1, but remember to flip the direction of the inequality sign:
25n ≥ 50
n ≥ 2
Joyce needs to visit the zoo at least 2 times to justify the expense of the membership fee.
So the answer is: a) 2.
To determine how many times Joyce will need to visit the zoo to justify the expense of the membership fee, we can compare the costs of visiting the zoo with and without the membership.
Without the membership:
The cost to visit the zoo each time is $45.
With the membership:
The cost to join the membership is $50, and then each visit to the zoo only costs $20.
To find the number of visits needed to justify the expense of the membership fee, we can set up an equation:
$45 x number of visits = $50 + $20 x number of visits.
Simplifying the equation:
$45 x number of visits = $50 + $20 x number of visits.
Rearranging the equation:
$45 x number of visits - $20 x number of visits = $50.
Combining like terms:
$25 x number of visits = $50.
Dividing both sides by $25:
number of visits = $50 / $25.
number of visits = 2.
Therefore, Joyce will need to visit the zoo 2 times to justify the expense of the membership fee.
The correct answer is: a) 2.
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 individual visits with the cost of having a membership.
Let's calculate the total cost of individual visits:
Joyce will pay $45 for each visit to the zoo, as stated in the question.
Now, let's calculate the cost of having a membership:
The membership fee is $50. Additionally, Joyce will now only need to pay $20 for each visit to the zoo.
To find out how many times Joyce will need to visit the zoo to justify the membership fee, we need to compare the total cost of individual visits with the cost of having a membership.
Let's do the calculation:
Total cost of individual visits = $45 * number of visits
Cost of having a membership = $50 + ($20 * number of visits)
To justify the membership fee, we need to find the number of visits where the cost of having a membership is equal to or less than the total cost of individual visits. In other words, we need to find the number of visits where:
$50 + ($20 * number of visits) <= $45 * number of visits
Let's solve the equation:
$50 + ($20 * number of visits) <= $45 * number of visits
$50 <= $45 * number of visits - $20 * number of visits
$50 <= $25 * number of visits
$50 / $25 <= number of visits
2 <= number of visits
Therefore, Joyce will need to visit the zoo at least 2 times to justify the expense of the membership fee.
So, the answer is:
a) 2