Integrated Math 1 Word Problem

Question

How do I solve this problem?: Tickets to the planetarium cost $11 for members of the planetarium's frequent visitor program and $13 for visitors who are not members of this program. Joining the frequent visitor program at the planetarium costs $5 per year. Use this information for Items 7-9.

7. Write an equation that can be used to determine n, the number of visits per year for which the cost of being a member of the frequent visitor program is equal to the cost of not being a member.

Answer 1

The annual cost for a non-member is the number of tickets (n) x price. So Cost = $13n

For a member, the cost would be $11n + $5 for membership.

We are asked how many visits does it take for the cost to be equal. Therefore we can say that the number of tickets, (n) is the same for both members and non members, and we want to know when the cost is the same, so we set the equations equal to one another.

$13n = $11n + $5. So n = 2.5 This means that the cost for 2 visits $26 for non - members and $27 for members is less expensive for a non-member, but for 3 visits, $39 non-members and $38 for members, it becomes cheaper for members. Of course you can't visit 2.5 times, but if you could, the Non-member cost would be $32.50 and for members, $32.50

So if you are planning on visiting more than twice, purchase an annual membership.