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?

tertre
Dec 29, 2017

#1

#4**0 **

nevermind I got it.

\((t+1)(3t-3)=(3t-5)(t+2)\)

Expanding gives

\(3t^2-3t+3t-3= 3t^2+6t-5t-10\)

Get the like terms together

\(3t^2-3t^2 -3t+3t +5t - 6t=-10+3\)

3t^{2} cuts out and the remaining equals to -t but u are looking for a positive t so so multiply both sides by (-).

therefore this gives

\(t=10-3\)

\(t=7\)

So on Tuesday, u worked 8 hours and got 18$ and Andrew worked 16 hours and got 9 dollars. And also the question should be

'At the end of the day, I had earned two times more than he had. What is the value of t?'

Rauhan
Dec 29, 2017

#7**+1 **

Hours * Rate per hour = Total Amt

So

(t + 1) (3t - 3) = (3t - 5)(t + 2) + 2 simplify

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

-3 = 1t - 8 add 8 to both sides

5 = 1t

5 = t

Check

(5 + 1)(3*5 - 3) = (3(5) - 5 ) ( 5 + 2) + 2 ???

(6)(12) = (10)(7) + 2

72 = 70 + 2

So.....t = 5 is correct

CPhill
Dec 29, 2017