Question

The johnson county carnival costs $15 plus .50 per ride zthe jefferson county carnival cost $10. plus 1.00 per ride. How many rides should you plan on riding to make the johnson county carnival less expensive than the jefferson county carnival.

Answer 1

let the number of rides for which one spends same amount of money in both carnivals = x
Then, for Johnson CC you spend amount = 15 + 0.50x
and for Jefferson CC you spend amount = 10 + x

since for x rides, both amounts r same
15 + 0.50x = 10 + x
15 - 10 = x - 0.50x
5 = 0.50x
5/0.50 = x
10 = x

This means that for 10 rides, you spend equal amount of money in both carnivals. However, after these 10 rides, any additional ride will cost 0.50 in Johnson than CC but 1.00 in Jefferson CC i.e. Jefferson CC becomes expensive than Johnson CC.

So, one should plan to take minimum 11 rides to make Johnson CC cheaper than Jefferson CC.