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On Monday, I worked t - 6  hours and earned 2t - 5 dollars per hour. My friend Andrew worked 2t - 8 hours but only earned  t - 5 dollars an hour. As it turns out, we earned the same amount. What is the value of t ?

matth99  Jul 2, 2018
 #1
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Multiply the hours that both of you worked x amount of money you earned per hour. Then equate them and solve for t as follows:

 

 (t - 6) * (2t - 5) = (2t - 8) * (t - 5), solve for t

 

(t - 6) (2 t - 5) = (t - 5) (2 t - 8)

Expand out terms of the left hand side:
2 t^2 - 17 t + 30 = (t - 5) (2 t - 8)

Expand out terms of the right hand side:
2 t^2 - 17 t + 30 = 2 t^2 - 18 t + 40

Subtract 2 t^2 - 18 t + 40 from both sides:
t - 10 = 0

Add 10 to both sides:
t = 10 

Guest Jul 2, 2018

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