Word problem

Question

To become a member at the zoo, you have to pay a $45 membership fee. The cost of admission to the zoo is $6 for members and $11 for nonmembers. After how many visits to the zoo is the total cost for members, including the membership fee, the same as the total cost for nonmembers?

Answer 1

Let's say I make x trips to the zoo.

 

If I am a member, I had to have paid the $45 membership fee. Then each time I visit, I pay $6. So if I make x trips, I have paid 6x dollars, not including the $45. So in total in x trips, I have actually spent $45+6x total dollars.

 

If I am not a member, I simply pay $11 per trip. So in x trips, I spend 11x dollars. 

 

The question asks when these are the same number. That is, when is

 

11x = 45 + 6x

 

So we need to solve for x. First, subtract 6x from both sides

 

11x = 45 + 6x

5x = 45

 

Now divide by 5

 

5x = 45

  x = 9

 

So the price would be the same after 9 trips. Note that if you plan on making more than 9 trips, you are actually saving money! And who wouldn't want to make at least 10 trips to the zoo to see the adorable penguins?!