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 $t$?
number of dollars you earned = (t + 1)(3t - 3)
number of dollars Andrew earned = (3t - 5)(t + 2)
number of dollars you earned = number of dollars Andrew earned + 2
(t + 1)(3t - 3) = (3t - 5)(t + 2) + 2
Multiply out (3t - 5)(t + 2) and (t + 1)(3t - 3)
3t2 - 3t + 3t - 3 = 3t2 + 6t - 5t - 10 + 2
Combine like terms.
3t2 - 3 = 3t2 + t - 8
Add 8 to both sides of the equation.
3t2 + 5 = 3t2 + t
Subtract 3t2 from both sides of the equation.
5 = t
number of dollars you earned = (t + 1)(3t - 3)
number of dollars Andrew earned = (3t - 5)(t + 2)
number of dollars you earned = number of dollars Andrew earned + 2
(t + 1)(3t - 3) = (3t - 5)(t + 2) + 2
Multiply out (3t - 5)(t + 2) and (t + 1)(3t - 3)
3t2 - 3t + 3t - 3 = 3t2 + 6t - 5t - 10 + 2
Combine like terms.
3t2 - 3 = 3t2 + t - 8
Add 8 to both sides of the equation.
3t2 + 5 = 3t2 + t
Subtract 3t2 from both sides of the equation.
5 = t