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 $t$?

Guest Jun 7, 2019

#1**+3 **

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)

3t^{2} - 3t + 3t - 3 = 3t^{2} + 6t - 5t - 10 + 2

Combine like terms.

3t^{2} - 3 = 3t^{2} + t - 8

Add 8 to both sides of the equation.

3t^{2} + 5 = 3t^{2} + t

Subtract 3t^{2} from both sides of the equation.

5 = t

hectictar Jun 7, 2019

#1**+3 **

Best Answer

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)

3t^{2} - 3t + 3t - 3 = 3t^{2} + 6t - 5t - 10 + 2

Combine like terms.

3t^{2} - 3 = 3t^{2} + t - 8

Add 8 to both sides of the equation.

3t^{2} + 5 = 3t^{2} + t

Subtract 3t^{2} from both sides of the equation.

5 = t

hectictar Jun 7, 2019