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GMATT73
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60 cookies were to be equally distributed to X campers. 23 Oct 2005, 04:58
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60 cookies were to be equally distributed to X campers. When 8 campers did not want the cookies, the other campers each received 2 more cookies. Which of the following equations could be used to find the number of campers X?

A. x^2-8x-240
B. x^2-8x+240
C. x^2+8x-240
D. x^2+8x+240
E. x^2-4x-120



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60 cookies were to be equally distributed to X campers. 23 Oct 2005, 05:12
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Express the quantities in cookies per camper and set the two scenarios equal.

initial cookies per camper 60/X

if 8 campers dont want cookies, than cookies per camper 60/x-8 + 2

Set those two equal and rearrange... I get to
2x^2 - 16x +240
x^2 - 8x + 240
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60 cookies were to be equally distributed to X campers. Updated on: 23 Oct 2005, 05:18
Originally posted by GMATT73 on 23 Oct 2005, 05:17.
Last edited by GMATT73 on 23 Oct 2005, 05:18, edited 1 time in total.
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Good work nero. Taking this problem a step further, can you solve the total number of campers?
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60 cookies were to be equally distributed to X campers. 23 Oct 2005, 05:25
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sorry, wrong, let's me try again :oops:
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60 cookies were to be equally distributed to X campers. 23 Oct 2005, 05:26
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nero44
Express the quantities in cookies per camper and set the two scenarios equal.

initial cookies per camper 60/X

if 8 campers dont want cookies, than cookies per camper 60/x-8 + 2

Set those two equal and rearrange... I get to
2x^2 - 16x +240
x^2 - 8x + 240
Show more


the method is correct but the equation is x^2-8x-240, Nero! :wink:
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60 cookies were to be equally distributed to X campers. 23 Oct 2005, 05:32
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Matt, there're many ways to solve quadratic equation.
1)Grab a calculator, set mode 1, fill the a, b, c of the quadratic equation into the calcutor, presse enter to get the result.
2) Find delta
3) since the number of campers must be integer .....the expected outcome of the equation must be among the factors of -240 ( including negative factors as well).
Since the equation is quadratic, possibly it has 2 outcomes and the absolute difference of these two outcomes is 8.
the minus sign in front of 8 indicates that the bigger out comes( in absolute value) is negative.
Now, have a glance at 240......such a pairs of outcome is -20 and 12
Then, we can write the equation like this : (x-20) (x+12)=0
easily find out x= 20

The explanation is wordy but in fact , the whole process of reasoning is very quick if you're familiar with this trick :wink:
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60 cookies were to be equally distributed to X campers. 23 Oct 2005, 06:03
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Agree... method 3) is what I usually use, if excel is not at hand (which certainly isn't the case during the gmat :P)

I guess it depends on how well you are familiar with numbers to see quadratic equations...

else -> PQ or ABC formula.. dont know how you guys call it. its the same thing but I heard different names for it ..
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60 cookies were to be equally distributed to X campers. 23 Oct 2005, 08:52
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how do you get x^2-8x-240?

I keep getting +240?

laxieqv
nero44
Express the quantities in cookies per camper and set the two scenarios equal.

initial cookies per camper 60/X

if 8 campers dont want cookies, than cookies per camper 60/x-8 + 2

Set those two equal and rearrange... I get to
2x^2 - 16x +240
x^2 - 8x + 240

the method is correct but the equation is x^2-8x-240, Nero! :wink:
Show more
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60 cookies were to be equally distributed to X campers. 23 Oct 2005, 09:13
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(60/X)+2=60/(X-8) where X-number of students
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60 cookies were to be equally distributed to X campers. 23 Oct 2005, 09:14
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fresinha12
how do you get x^2-8x-240?

I keep getting +240?

laxieqv
nero44
Express the quantities in cookies per camper and set the two scenarios equal.

initial cookies per camper 60/X

if 8 campers dont want cookies, than cookies per camper 60/x-8 + 2

Set those two equal and rearrange... I get to
2x^2 - 16x +240
x^2 - 8x + 240

the method is correct but the equation is x^2-8x-240, Nero! :wink:
Show more


The initial portion each gets is : 60/x
After receive 2 more, each receives (60/x)+2
we have : 60/x +2 = 60/(x-8)
Then you get A correct.
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60 cookies were to be equally distributed to X campers. 23 Oct 2005, 09:46
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laxieqv
fresinha12
how do you get x^2-8x-240?
I keep getting +240?
laxieqv
nero44
Express the quantities in cookies per camper and set the two scenarios equal.
initial cookies per camper 60/X
if 8 campers dont want cookies, than cookies per camper 60/x-8 + 2
Set those two equal and rearrange... I get to
2x^2 - 16x +240
x^2 - 8x + 240
the method is correct but the equation is x^2-8x-240, Nero! :wink:
The initial portion each gets is : 60/x
After receive 2 more, each receives (60/x)+2
we have : 60/x +2 = 60/(x-8)
Then you get A correct.
Show more


laxieqv does everything in a very simple manner...
before:
each camper's share=60/x

after, 8 campers denied cookies:
the no of cookies for 8 campers=8(60/x)
so divide 8(60/x) among the remaining cmpers (x-8) which should equal to 2 = (480/x)/(x-8)

so after simplification, x^2-8x-240=0
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60 cookies were to be equally distributed to X campers. 24 Oct 2005, 13:01
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Quote:
how do you get x^2-8x-240?

I keep getting +240?
Show more


Here's the step-by-step process:

60/(x-8) = (60/x) + 2
60/(x-8) = (60+2x)/x

cross multiply:

60x = 60x-480+2x^2-16x

the 60x's cancel out, leaving you with:
2x^2 - 16x- 480 = 0

you can divide the equation by two to get:

x^2 - 8x - 240



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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