Problem Solving

In a certain warehouse, 60% of the packages weigh less than 75 pounds, and a total of 48 packages weigh less than 25 pounds. If 80% of the packages weight atleast 25 pounds, how many of the packages weigh at least 25 pounds but less than 75 pounds:

1)8
2)64
3)96
4)102
5)144

Thank you,
Prerna

prernamalhotra wrote:In a certain warehouse, 60% of the packages weigh less than 75 pounds, and a total of 48 packages weigh less than 25 pounds. If 80% of the packages weight atleast 25 pounds, how many of the packages weigh at least 25 pounds but less than 75 pounds:

1)8
2)64
3)96
4)102
5)144

Thank you,
Prerna

Since 80% of the packages weigh at least 25 pounds, we get:
(at least 25 pounds) : (less than 25 pounds) = 80:20 = 4:1.

Since 48 packages weigh less than 25 pounds, the MULTIPLIER for the ratio is 48:
(at least 25 pounds) : (less than 25 pounds) = (48*4) : (48*1) = 192:48.
Thus, the total number of packages = 192+48 = 240.

Since 60% of the packages weigh less than 75 pounds, 40% of the 240 packages weigh at least 75 pounds:
(40/100)(240) = 96.

Thus:
Packages that weigh at least 25 pounds but less than 75 pounds = (total) - (less than 25 pounds) - (at least 75 pounds) = 240-48-96 = 96.

The correct answer is C.

Pictorial presentation of explanation