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A sports retailer ordered white and yellow tennis balls

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A sports retailer ordered white and yellow tennis balls [#permalink] New post 21 Feb 2013, 07:15
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A sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 50 extra yellow balls and making ratio of white balls to yellow balls 8/13. How many tennis balls did the retailer order originally.

A. 180
B. 130
C. 140
D. 160
E. 120
[Reveal] Spoiler: OA
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Re: A sports retailer ordered white and yellow tennis balls [#permalink] New post 21 Feb 2013, 07:21
Expert's post
antoxavier wrote:
A sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 50 extra yellow balls and making ratio of white balls to yellow balls 8/13. How many tennis balls did the retailer order originally.

A. 180
B. 130
C. 140
D. 160
E. 120


White:Yellow = x:(x+50) = 8:13 --> 13x = 8x + 400 --> x = 80.

The total # of balls originally x + x = 80 + 80 = 160.

Answer: D.
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Re: A sports retailer ordered white and yellow tennis balls [#permalink] New post 21 Feb 2013, 07:30
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Bunuel wrote:

White:Yellow = x:(x+50) = 8:13 --> 13x = 8x + 400 --> x = 80.

The total # of balls originally x + x = 80 + 80 = 160.

Answer: D.


Bunuel's algebraic solution above is perfectly correct. You can also solve this question using the concept if you don't like algebra or if you think it's faster:

The ratio of white:yellow balls was supposed to be even, i.e. 1:1 or 2:2 or 8:8, before the extra 50 yellow balls arrived. This means that the number of white balls is unchanged in the new ratio so 8:13 implies that the difference between 13 and 8 (aka 5 units) is representing 50 yellow balls. Each unit in this ratio thus represents 10 balls of indiscriminate colour, making the original 8:8 ratio represent 80 white balls and 80 yellow balls: 160 overall. Answer D.

Algebra never fails in these problems but it is time-consuming for some people, so if you can solve a question multiple ways, you're more flexible on test day to solve tricky or new question types.

Hope this helps
-Ron
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Re: A sports retailer ordered white and yellow tennis balls   [#permalink] 21 Feb 2013, 07:30
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A sports retailer ordered white and yellow tennis balls

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