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yaron
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AVG question 13 Aug 2005, 04:50
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Hi all,
1st time here so I just wanted to say that I find this site extremely helpful!

Here is an AVG question that I could not figure out:

A bag of 216 caramels is divided equally among a group of children. if 6 children were added to the group, each child would receive 3 fewer caramels. How many children are currently in the group?

a. 36
b. 24
c. 20
d. 18
e. 12

Thanks in advance!



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AJB77
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AVG question 13 Aug 2005, 05:15
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Backsolving is best for these types of problems.

If x is the number of children and y is the number of caramels that they currently get as a share, we have

xy = 216 = (x+6)(y-3)

Plug in the choices and see that x=18 is the answer.

18 * 12 = 216 = (18+6) * (12-3)
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yaron
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AVG question 13 Aug 2005, 05:48
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Thanks! Any shortcuts?
Doing it that way could be a time killer sometimes…
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ywilfred
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AVG question 13 Aug 2005, 06:11
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yaron
Thanks! Any shortcuts?
Doing it that way could be a time killer sometimes…
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Plugging in this case is efficient since you would end up with a quadratic equation if you attempt to solve by algebra. You would get this quadratic equation:

n^2 - 6n - 648 = 0 where n is the number of students. 648 is a big number to solve for quadratic equations and it could take some time.

One way to improve efficiency for plugging in numbers would be to start with the middle number. In this case, it's 20. If the solution is wrong then you know where to adjust (i.e. choose a larger number or a smaller number). It's more efficient this way than to plug in numbers starting from A to E.
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yaron
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AVG question 13 Aug 2005, 06:21
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Got it.
Thanks alot!
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Dan
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AVG question 13 Aug 2005, 06:29
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yaron
Hi all,
1st time here so I just wanted to say that I find this site extremely helpful!

Here is an AVG question that I could not figure out:

A bag of 216 caramels is divided equally among a group of children. if 6 children were added to the group, each child would receive 3 fewer caramels. How many children are currently in the group?

a. 36
b. 24
c. 20
d. 18
e. 12

Thanks in advance!
Show more


216/(x+6) = 216/x - 3

multiply by x(x+1) ==>

x^2+6x-432 = 0

complete the square,

==> (x+3)^2 = 441

==> x = -3 +/- 21

x = 18 or x = -24 (no)

so x = 18.
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yaron
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AVG question 13 Aug 2005, 06:44
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Dan
yaron
Hi all,
1st time here so I just wanted to say that I find this site extremely helpful!

Here is an AVG question that I could not figure out:

A bag of 216 caramels is divided equally among a group of children. if 6 children were added to the group, each child would receive 3 fewer caramels. How many children are currently in the group?

a. 36
b. 24
c. 20
d. 18
e. 12

Thanks in advance!

216/(x+6) = 216/x - 3

multiply by x(x+1) ==>

x^2+6x-432 = 0

complete the square,

==> (x+3)^2 = 441

==> x = -3 +/- 21

x = 18 or x = -24 (no)

so x = 18.
Show more


:-) WOW, that's a good one. (I guess you meant "multiply by: x(x+6)")



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!