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?

Answer 1

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.