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# Help

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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

#1
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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
+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

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