likar wrote:
Pat, Kate, and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much time 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
We can see that Kate charged the fewest hours, so...
Let x =the number of hours Kate charged
Pat charged twice as much time to the project as KateSo,
2x = the number of hours Pat charged
Pat charged 1/3 as much times as MarkIn other words, Mark charged THREE TIMES as much time as Pat
So, 3(
2x ) = the number of hours Mark charged
In other words,
6x = the number of hours Mark charged
Pat, Kate and Mark charged a total of 162 hours to a certain project. We can write: x +
2x +
6x = 162
Simplify: 9x = 162
Solve: x = 18
So, Kate charged
18 hours
When we plug x = 18 into
6x, we see that Mark charged
108 hours
How many more hours did Mark charge to the project than Kate? Answer =
108 -
18= 90
= D
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