On Tuesday, I worked \(t+1\) hours and earned \(3t-3\) dollars per hour. My friend Andrew worked \(3t-5\) hours but only earned \(t+2\) dollars an hour. At the end of the day, I had earned two dollars more than he had. What is the value of \(t\) ?
We have this
(t + 1) (3t - 3) = (3t - 5) (t + 2) + 2 simplify
3t^2 - 3 = 3t^2 + t - 10 + 2 subtract 3t^2 from both sides and simplify
-3 = t - 8 add 8 to both sides
5 = t