In a certain warehouse, 60 percent of the packages weigh les

ktrout2020 wrote:In a certain warehouse, 60 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?

A. 8
B. 64
C. 96
D. 102
E. 144

Source: Kaplan

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: 0.2T = 48
Solve: T = 240

60% of the packages weigh less than 75 pounds
So, 60% of T = number of packages that weigh less than 75 pounds
60% of 240 = 144, so 144 packages weigh less than 75 pounds

OF THOSE 144 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 = 144 - 48 = 96

Answer: C

Cheers,
Brent

ktrout2020 wrote:In a certain warehouse, 60 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?

A. 8
B. 64
C. 96
D. 102
E. 144

Source: Kaplan

Since 80 percent of the packages weigh at least 25 pounds, 20% weigh less than 25 pounds. We are given that there are 48 such packages. Thus, if we let n = the total number of packages, we can create the equation:

0.2n = 48

n = 240

Since 60 percent of the packages weigh less than 75 pounds, we have 0.6 x 240 = 144 packages weigh less than 75 pounds, and, therefore, there must be 144 - 48 = 96 packages that weigh at least 25 pounds but less than 75 pounds.

Answer: C