In a certain warehouse, 40 percent of the packages weigh less than 75 pounds, and a total of 48 packages weigh less than 25 pounds. If 80 percent of the packages weigh at least 25 pounds, how many of the packages weigh at least 25 pounds but less than 75 pounds?
Options.
A) 8
B) 64
C) 48
D) 102
E) 144

Rationale: "if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 40 % of the packages weigh less than 75 pounds so , 40 % oft = number of packages that weigh less than 75 pounds 40 % of 240 = 96 , so 96 packages weigh less than 75 pounds of those 96 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 96 - 48 = 48 = c"
Answer: C