How to do using weighted average ?

[Uva@90]

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

[[email protected]]

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

[talaangoshtari]

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

[Brent@GMATPrepNow]

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@GMATPrepNow]

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

[Uva@90]

Thanks Rich. I got your explanation.


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

Regards,
Uva