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avatar+1364 

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
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7+0 Answers

 #1
avatar+502 
0

I am not 100% sure if this answer is correct but is the answer \(\frac{7}{6}\)

Rauhan  Dec 29, 2017
 #2
avatar+502 
0

If it is then I will explain how I got it.

Rauhan  Dec 29, 2017
 #3
avatar+1364 
0

i don't think so

tertre  Dec 29, 2017
 #4
avatar+502 
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

 

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

 

3t2 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
 #5
avatar+1364 
+1

nope, t=5

tertre  Dec 29, 2017
 #6
avatar+502 
0

substituting 5 in the question doesn't give 2 times the dollars

Rauhan  Dec 29, 2017
 #7
avatar+81022 
+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

 

 

 

cool cool cool

CPhill  Dec 29, 2017

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