Pat mark and kate charged a total of 162 hours

[HeyArnold]

Pat, Kate and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?
A. 18
B. 36
C. 72
D. 90
E. 108





I understand that you can use a single variable here, but I chose to set Pat as the variable (since the question phrases everyone in relation to pat)

So I said:

Pat = X
Kate = 1/2 X
Mark = 3X

4.5X = 162... clearly this didn't work out, why doesn't this work? As opposed to saying:

Kate = X
Pat = 2X
Mark = 6X

9X = 162 gives the correct answer!

[neelgandham]

Pat, Kate and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?
A. 18
B. 36
C. 72
D. 90
E. 108

I understand that you can use a single variable here, but I chose to set Pat as the variable (since the question phrases everyone in relation to pat)

So I said:

Pat = X
Kate = 1/2 X
Mark = 3X

4.5X = 162... clearly this didn't work out, why doesn't this work?

It works, it is just that you stopped it there
4.5X = 162
=> 9X = 324
=> X = 36

So Mark charged 3X = 3*36 = 108
and Kate charged 0.5X = 18
So, Answer = 3x-0.5x = 90

As opposed to saying:

Kate = X
Pat = 2X
Mark = 6X

9X = 162 gives the correct answer!
=> X = 18
=> Mark = 6X = 6*18 = 108
=> Kate = X = 18
So answer = 6X-X = 90

Please find the answer in Bold ! Let me know if you still need help in understanding ?

[GMATGuruNY]

Pat, Kate and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?
A. 18
B. 36
C. 72
D. 90
E. 108





I understand that you can use a single variable here, but I chose to set Pat as the variable (since the question phrases everyone in relation to pat)

So I said:

Pat = X
Kate = 1/2 X
Mark = 3X

4.5X = 162... clearly this didn't work out, why doesn't this work?

The approach above is fine.
x = 162/4.5 = 36.
Mark = 3x = 3*36 = 108.
Kate = (1/2)x = (1/2)*36 = 18.
Mark-Kate = 108-18 = 90.

I would plug in values.

Let Mark = 6.
Pat = (1/3)*6 = 2.
Since Pat charges twice Kate, Kate = 1.
Thus, Mark : Pat : Kate = 6:2:1.

Since 6+2+1 = 9, and 162/9 = 18, all of the values in the ratio must be multiplied by 18:
Mark : Pat : Kate = 18*(6:2:1) = 108:36:18.

Mark-Kate = 108-18 = 90.

The correct answer is D.