How to do using weighted average ?

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Thu Jul 02, 2015 8:44 am

A girl scout was selling boxes of cookies. In a month, she sold both boxes of chocolate chip cookies ($1.25 each) and boxes of plain cookies ($0.75 each). Altogether, she sold 1585 boxes for a combined value of $1588.75. How many boxes of plain cookies did she sell?

(A) 0

(B) 285

(C) 500

(D) 695

(E) 785

How to do using Weighted average method ?

Thanks.
Regards,
Uva

Known is a drop Unknown is an Ocean

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Source: Beat The GMAT — Problem Solving | Thu Jul 02, 2015 8:44 am

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by [email protected] » Thu Jul 02, 2015 10:02 am

Hi Uva@90,

When it comes to Weighted Average questions, there are several different ways to go about getting to the correct answer. This question has some rather specific patterns that you can take advantage of though... so that you can avoid doing lots of math.

First off, the answer choices are "spaced out", so we can take advantage of that spread.

Second, the average of 1 box of chocolate chip cookies and 1 box of plain cookies is ($1.25 + $0.75)/2 = $1. This is important because....

Third, there are 1585 boxes of cookies with a combined value of $1588.75.....

1588.75/1585 = Just a little bit more than $1 per box

This means that SLIGHTLY MORE than half of the boxes are chocolate chip cookies. We're asked how many boxes of PLAIN cookies were sold (thus, SLIGHTLY LESS than half of those boxes were plain cookies.

Half of 1585 is about 792. Which answer is slightly less than that....?

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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talaangoshtari: Master | Next Rank: 500 Posts; Posts: 154; Joined: Wed May 21, 2014 4:29 amFollowed by: 1 member; Thanked: 8 times

by talaangoshtari » Thu Jul 02, 2015 10:03 am

Let
c:chocolate chip cookies
p:plain cookies

p + c = 1585
1.25c + .75p = 1588.75

Therefore we have,
1.25(1585 - p) + .075p = 1588.75
=> p = 785

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Jul 02, 2015 10:11 am

In my opinion, Rich's solution is definitely the fastest/easiest approach.

If you're interested, we have a free video that covers the concepts that Rich applied in his solution: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Here are some additional practice questions related to weighted averages:
- https://www.beatthegmat.com/weighted-ave ... 17237.html
- https://www.beatthegmat.com/weighted-ave ... 14506.html
- https://www.beatthegmat.com/average-weig ... 57853.html
- https://www.beatthegmat.com/averages-que ... 87118.html

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Jul 02, 2015 10:22 am

Uva@90 wrote:A girl scout was selling boxes of cookies. In a month, she sold both boxes of chocolate chip cookies ($1.25 each) and boxes of plain cookies ($0.75 each). Altogether, she sold 1585 boxes for a combined value of $1588.75. How many boxes of plain cookies did she sell?

(A) 0

(B) 285

(C) 500

(D) 695

(E) 785

Here's the setup for a lonnnnnngggg approach:

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

let x = # of plain cookies
So, 1585 - x = # of chocolate chip cookies

Plugging in the values, we get: ($1588.75)/1585 = (x/1585)($0.75) + [(1585-x)/1585][$1.25]

Solve for x.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Thu Jul 02, 2015 9:07 pm

Thanks Rich. I got your explanation.

Brent,
Thanks for the extra quetsions. It helped me a lot.

Regards,
Uva

Known is a drop Unknown is an Ocean

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