+0

# binomials

0
47
7
+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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#1
+502
0

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

Rauhan  Dec 29, 2017
#2
+502
0

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

Rauhan  Dec 29, 2017
#3
+1364
0

i don't think so

tertre  Dec 29, 2017
#4
+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
+1364
+1

nope, t=5

tertre  Dec 29, 2017
#6
+502
0

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

Rauhan  Dec 29, 2017
#7
+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

CPhill  Dec 29, 2017

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