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
How to do using weighted average ?
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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
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
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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
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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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
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
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Here's the setup for a lonnnnnngggg approach: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
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