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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 $t$?

 Jun 7, 2019

Best Answer 

 #1
avatar+8829 
+4

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

 Jun 7, 2019
edited by hectictar  Jun 8, 2019
 #1
avatar+8829 
+4
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)

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

hectictar Jun 7, 2019
edited by hectictar  Jun 8, 2019

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