Question

Joining the frequent visitor program at the planetarium costs $5 per year. 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

Frequent visitor admission fee: $5/year

Non-member, one-time admission fee: c/visit

Equate these: $5/year = (c/visit)(n visits per year)

If, for example, the one-time admission fee is $2, then $5/year = ($2/visit)(n visits). (Here, c=2.) n comes out to 2 1/2 visits, which of course doesn't make sense, since the number of visits is always an integer (whole number).

Another example: If the one-time admission fee is $1, then $5/year = ($1/visit)(n visits). Here, $5 = $1n, and n = $5/$1 = 5 visits. Here c = $1. This makes sense.