Caleb is planning a visit to an amusement park. he wants to figure out how many roller coasters he could ride and how many shows he can watch in 345 minutes. each roller coaster takes 5 minutes to ride. he estimates that the average wait time for a roller coaster is 30 minutes. caleb wants to ride 3 more roller coasters than the number of shows he watches. each show takes 25 minutes. in 345 minutes, he can ride roller coasters and watch shows.

Let r and s represent the number of times Caleb can ride the roller coaster and watch a show, respectively. The time Caleb needs to allow for each roller coaster ride is (wait time) + (ride time) = (30 +5) min = 35 min. Then we can write the equations
  r - s = 3
  35r +25s ≤ 345

Adding 25 times the first equation to the second, we get
  25(r -s) +(35r +25s) ≤ 25(3) +(345)
  60r ≤ 420 . . . . . . collect terms
  r ≤ 7 . . . . . . . . . . . divide by 60

Caleb can ride a maximum of 7 roller coasters and watch 4 shows in 345 minutes.


The problem can obviously be worked using two equations instead of one equation and an inequality. It isn't clear until the final answer that the number of minutes comes out exactly the amount needed, which is why we chose an inequality.