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In a certain warehouse, 60 percent of the packages weigh less than 75

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In a certain warehouse, 60 percent of the packages weigh less than 75  [#permalink]

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New post 28 Dec 2004, 21:52
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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
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Re: In a certain warehouse, 60 percent of the packages weigh less than 75  [#permalink]

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New post 25 Sep 2015, 08:50
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kdhong 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


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 = C

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Brent
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Re: In a certain warehouse, 60 percent of the packages weigh less than 75  [#permalink]

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New post 30 Dec 2004, 17:58
C
60% < 75 lbs; 48 < 25lbs &
80% >= 25lbs, so 20% = 48packages
Total no. of packages = 240
since 60% < 75 lbs which is 144packages and
48packages < 25 lbs. The required result is 144 - 48 = 96
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Re: In a certain warehouse, 60 percent of the packages weigh less than 75  [#permalink]

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New post 25 Sep 2015, 06:12
1
sharmasneha wrote:
In a certain warehouse, 60 % of the packages weigh less than 75 lbs, and a total of 48 packages weigh less than 25 lbs. If 80% of the packages weigh at least 25 pounds, how many packages weigh at least 25 lbs but less than 75 lbs.

a)8
b)64
c)96
d)102
e)144


hello,
80% weigh atleast 25, so 20% weigh less than 25, equal to 48 packages...
so 20%=48..
now packages that weigh between 25 and 75= 60%-20%=40%...
since 20%=48, 40%=96..
C
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Re: Word problem  [#permalink]

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New post 26 Sep 2018, 10:00
I got C, based on below calculations.

Let total number of packages be x

>75lbs= 60% of x, based on the question stem, the following are the parts that together make it 60% of x: includes 48 packages that are less than 25lbs and 80% that are at least 25 lbs (and above).
Question basically is asking for the bold part.
I am writing this equations as .6x=.8(.6x)+48
Solve for x= .6x- (.8P*.6x)= 48---- x=400.
.6x= 120
and .8(120)= 96.
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Re: In a certain warehouse, 60 percent of the packages weigh less than 75  [#permalink]

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New post 02 Oct 2018, 18:21
kdhong 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


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
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Re: In a certain warehouse, 60 percent of the packages weigh less than 75  [#permalink]

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New post 16 Jan 2020, 05:13
kdhong 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


<-------------------- 60% --------------------------
0 ........... 25 .............................................. 75 .......... 100
/////////////----------------------- 80% -------------------------->

Since 80% packages weight at least 25 pounds, 20% weight less than 25 pounds.

<-------------------- 60% ---------------------------
0 ........... 25 .............................................. 75 .......... 100
<---20%-><----------------------- 80% ------------------------>

These 20% are equivalent to 48 packages.

Now, of the 60% packages that weight less than 75 pounds, 20% weight less than 25 pounds. So 40% weigh between 25 pounds and 75 pounds.
Since 20% is 48 packages, 40% will be 96 packages.

Answer (C)
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Re: In a certain warehouse, 60 percent of the packages weigh less than 75   [#permalink] 16 Jan 2020, 05:13

In a certain warehouse, 60 percent of the packages weigh less than 75

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