You've decided to take up kayaking. You can either buy your kayak for $197 and pay $8 every time you launch it or you can rent a kayak for a one time fee of a $10 security deposit and pay $25 per launch. After how many days/launches will it not matter whether you rent or buy? Assume you only kayak once a day

Let's represent this with two equations, with C(r) representing cost of buying, x representing each day you launch, C(r) representing cost of renting.

Cost of buying = 197 + 8x

C(b) = 198 + 8x

Cost of renting = 10 + 25x

C(r) = 10 + 25x

The question asks us when it will not matter. This means that we want to find when the cost is equal for renting and buying. So set these equations equal:

198 + 8x = 10 + 25x

Subtract 10 from both sides:

188 + 8x = 25x

Subtract 8x from both sides:

188 = 17x

Divide both sides by 17:

188/17 = x

x = 11.06, round this up to 12 days. (At the 11th day, it still matters.)

It will not matter after 12 launches.