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# Jim picked a number of pears, each of which he sold, canned, or poache

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
Jim picked a number of pears, each of which he sold, canned, or poache  [#permalink]

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09 Jul 2015, 03:25
4
7
00:00

Difficulty:

75% (hard)

Question Stats:

62% (02:41) correct 38% (02:43) wrong based on 165 sessions

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Jim picked a number of pears, each of which he sold, canned, or poached. If he canned 40 percent more than he poached, and he poached 60 percent less than he sold, approximately what percent of the pears did he sell?

A. 30%
B. 33%
C. 42%
D. 49%
E. 51%

Kudos for a correct solution.

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Re: Jim picked a number of pears, each of which he sold, canned, or poache  [#permalink]

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09 Jul 2015, 03:44
1
Let the number of sold pears be 100.
Then,the no of poached pears will be -40
and no of canned pears will be -140/100 * 40= 56
so total pears = 100+ 40+ 56 = 196
Sold%= 100/196 * 100 =51 approx
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Re: Jim picked a number of pears, each of which he sold, canned, or poache  [#permalink]

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09 Jul 2015, 03:47
3
Bunuel wrote:
Jim picked a number of pears, each of which he sold, canned, or poached. If he canned 40 percent more than he poached, and he poached 60 percent less than he sold, approximately what percent of the pears did he sell?

A. 30%
B. 33%
C. 42%
D. 49%
E. 51%

Kudos for a correct solution.

Let S,C and P represent the amount sold, canned or poached.

Given, C=1.4P and P=0.4S---> C=0.56 S

Thus % of sold pears = S / (S+C+P) = 1/1.96 = 51%, thus E is the correct answer,
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Re: Jim picked a number of pears, each of which he sold, canned, or poache  [#permalink]

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09 Jul 2015, 09:45
1
Bunuel wrote:
Jim picked a number of pears, each of which he sold, canned, or poached. If he canned 40 percent more than he poached, and he poached 60 percent less than he sold, approximately what percent of the pears did he sell?

A. 30%
B. 33%
C. 42%
D. 49%
E. 51%

Kudos for a correct solution.

Sold : Poched : Canned
100 : 40 : 56

100/196*100
If 196 is taken as 200, then 100/196*100>50% (100/200*100=50%)
Approx 51%

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Joined: 02 Sep 2009
Posts: 50627
Re: Jim picked a number of pears, each of which he sold, canned, or poache  [#permalink]

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13 Jul 2015, 01:32
Bunuel wrote:
Jim picked a number of pears, each of which he sold, canned, or poached. If he canned 40 percent more than he poached, and he poached 60 percent less than he sold, approximately what percent of the pears did he sell?

A. 30%
B. 33%
C. 42%
D. 49%
E. 51%

Kudos for a correct solution.

800score Official Solution:

Let p = the number of pears Jim poached. Since he canned 40% more than he poached, p + 0.4p = 1.4p is the number of pears that Jim canned. Furthermore, because he poached 60% less than what he sold, (1 – 0.6) × (number he sold) = p, or number he sold = p/0.4 = p/(4/10) = p × (10/4) = 2.5p. Adding up these values, we can figure out that Jim picked p + 1.4p + 2.5p = 4.9p pears in all. The percent of pears that he sold = (the number of pears sold)/(total number of pears) = 2.5p/4.9p = 2.5/4.9 = approximately 51%.
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Re: Jim picked a number of pears, each of which he sold, canned, or poache  [#permalink]

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25 Sep 2016, 05:42
Bunuel wrote:
Jim picked a number of pears, each of which he sold, canned, or poached. If he canned 40 percent more than he poached, and he poached 60 percent less than he sold, approximately what percent of the pears did he sell?

A. 30%
B. 33%
C. 42%
D. 49%
E. 51%

Kudos for a correct solution.

Let no of item sold be 100

Quote:
he poached 60 percent less than he sold

No of items poached is 40

Quote:
If he canned 40 percent more than he poached

No of items caned is 56

Total No of items is 196 ( 100 + 40 + 56 )

Quote:
approximately what percent of the pears did he sell?

Approx % sold = $$\frac{100}{196} *100$$ ~ 51%

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Re: Jim picked a number of pears, each of which he sold, canned, or poache  [#permalink]

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28 Feb 2018, 10:12
Bunuel wrote:
Jim picked a number of pears, each of which he sold, canned, or poached. If he canned 40 percent more than he poached, and he poached 60 percent less than he sold, approximately what percent of the pears did he sell?

A. 30%
B. 33%
C. 42%
D. 49%
E. 51%

Kudos for a correct solution.

We can let S = the number of pears he sold, C = the number of pears he canned, and P = the number of pears he poached and create the equations:

C = 1.4P

and

P = 0.4S

P/0.4 = S

10P/4 = S

5P/2 = 2.5P = S

The percent of pears he sold is:

(2.5P)/(1.4P + P + 2.5P)

2.5P/4.9P = 25/49, which is slightly more than 50%.

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Re: Jim picked a number of pears, each of which he sold, canned, or poache  [#permalink]

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16 Sep 2018, 09:21
did using ratio
can:packed:sold = 14:10:25
25k/49k
10% = 4.9 rounding to 5
50% = 50 so answer will be more then 50%
Re: Jim picked a number of pears, each of which he sold, canned, or poache &nbs [#permalink] 16 Sep 2018, 09:21
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