Question

Erin is considering joining one of 2 swim clubs. The Gators Swim Club has no registration fee, but charges $105 per month. The Tidal Wave Swim Club charges members $80 per month plus a one-time registration fee of $375. For how many months is Gators the cheaper option? Use system of equations and define variables

Answer 1

14 months

Explanation:

Given

Gator's = $105 monthly charges

Tidal Wave = $375 registration fee + $80 monthly charged

Required

Determine for how many months Gators is cheaper

Let the number of months be x;

Represent the given data, algebraically.

For Gators: 105x

For Tidal Wave: 375 + 80x

Represent the above as a n inequality

Since Gators has to be cheaper; we have

`105x < 375 + 80x`

Collect Like Terms

`105x - 80x < 375`

`25x < 375`

Divide both sides by 25

`x < 15`

This implies that Gator's will be cheaper for months less than 15

Hence, the number of months is 14