All 250 files on Sam's hard drive are infected

lheiannie07 wrote:All 250 files on Sam's hard drive are infected by either a virus or a worm or both. The number of files that are infected only by a worm is 2.5 times the number of files that are infected by both a virus and a worm. If 50% of the files were not infected by a virus, how many of Sam's files were NOT infected by a worm?

A. 50
B. 70
C. 75
D. 100
E. 125

Can some experts show me how to solve this?

OA C

I would set up the following diagram and equations, then solve as shown:

lheiannie07 wrote:All 250 files on Sam's hard drive are infected by either a virus or a worm or both. The number of files that are infected only by a worm is 2.5 times the number of files that are infected by both a virus and a worm. If 50% of the files were not infected by a virus, how many of Sam's files were NOT infected by a worm?

A. 50
B. 70
C. 75
D. 100
E. 125

etting b = the number of files infected by both a virus and a worm, we can create the equation:

Total = worm only + virus only + both + neither

250 = 2.5b + [0.5(250) - b] + b + 0

250 = 2.5b + 125

125 = 2.5b

50 = b

The files that were not infected by a worm were those that were infected by a virus only, so there were 0.5(250) - 50 = 125 - 50 = 75 files infected by virus only.

Answer: C