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A sporting goods store ordered an equal number of white and yellow ten

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srichaks
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A sporting goods store ordered an equal number of white and yellow ten [#permalink] New post   07 May 2010, 21:21
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A sporting goods store ordered an equal number of white and yellow tennis balls. The tennis ball company delivered 30 extra white balls, making the ratio of white balls to yellow balls 6:5. How many tennis balls did the store originally order?

A. 120
B. 150
C. 180
D. 300
E. 330

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I got the OA correct but wanted to see if this alternate method explanation makes sense:

The store originally ordered an equal number of white and yellow balls, they ended up with a white to yellow ratio of 6:5. This means for every 5 yellow balls, they got 6 white balls or they got 1/5 more white balls than yellow balls.. Can someone please explain the logic/steps for the preceding bold statement as to how it would be 1/5 more white balls?

Thanks in advance.
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Re: A sporting goods store ordered an equal number of white and yellow ten [#permalink] New post   07 May 2010, 22:50
Hi,

Initial ratio W/Y=1
new ratio (w+30)/y=6/5, or substituting w for y you get 6w=5w+150 or w=150.
then y=150, so the shop ordered 300 balls initially, 150 each
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Re: A sporting goods store ordered an equal number of white and yellow ten [#permalink] New post   08 May 2010, 00:06
I'll see if I can explain this well enough.

Initially, we get the same amount of white and yellow balls, or a 1:1 ratio. If 30 white are added, then the ratio of white to yellow becomes 6:5.

Let's take some other number, and say that we originally have 15 white and 15 yellow. Now, since in this case they are at a 5:5 ratio, we can say that for every 3 white balls there are 3 yellow balls. Now, if we add 1/5 the number of original white balls (3) to the original number of white balls (15) we get:

3 + 15 = 18

Remember, we still have only 15 yellow balls. Now what is the ratio? 18:15, or, if we reduce, 6:5. Hope this helps!
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Re: A sporting goods store ordered an equal number of white and yellow ten [#permalink] New post   08 May 2010, 08:08
Thanks Span!. Excellent explanation..!! got it.
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Re: A sporting goods store ordered an equal number of white and yellow ten [#permalink] New post   08 May 2010, 09:18
(X+30)/(X)= 6/5

Cross multiply: 5X + 150 = 6X
X = 150

And since we originally ordered 2X balls the answer is 300.
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Re: A sporting goods store ordered an equal number of white and yellow ten [#permalink] New post   11 Sep 2016, 06:09
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Quick approach:

The updated ratio is 6:5 implies that the total number of balls delivered by the company has to be a multiple of 11 (6+5).

Now, add 30 (extra ball count delivered by the company) to each of the options and look for the multiple of 11.

Note: This option works better in this case because we can easily look for a number which is a multiple of 11 and no more than 1 option fits the bill
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Re: A sporting goods store ordered an equal number of white and yellow ten [#permalink] New post   04 May 2018, 10:33
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srichaks wrote:
A sporting goods store ordered an equal number of white and yellow tennis balls. The tennis ball company delivered 30 extra white balls, making the ratio of white balls to yellow balls 6:5. How many tennis balls did the store originally order?

A. 120
B. 150
C. 180
D. 300
E. 330


We can let the number of white balls = the number of yellow balls = b; thus:

(b + 30)/b = = 6/5

5(b + 30) = 6b

5b + 150 = 6b

150 = b

The company originally ordered 300 balls.

Answer: D
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A sporting goods store ordered an equal number of white and yellow ten [#permalink] New post   28 Mar 2023, 17:55
Here is a simple method:

Adding 30 extra balls makes the ratio 6:5. If the 30 balls weren't added, the ratio would be 1:1 or 5:5
So each 1 in the ratio stands for 30 balls. Therefore, 5 would stand for 5*30=150 balls
Therefore, the original no.of balls ordered would be 150*2=300

Hope this helps!
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Re: A sporting goods store ordered an equal number of white and yellow ten [#permalink] New post   28 Mar 2023, 22:42
Expert Reply
srichaks wrote:
A sporting goods store ordered an equal number of white and yellow tennis balls. The tennis ball company delivered 30 extra white balls, making the ratio of white balls to yellow balls 6:5. How many tennis balls did the store originally order?

A. 120
B. 150
C. 180
D. 300
E. 330

Show Spoiler
I got the OA correct but wanted to see if this alternate method explanation makes sense:

The store originally ordered an equal number of white and yellow balls, they ended up with a white to yellow ratio of 6:5. This means for every 5 yellow balls, they got 6 white balls or they got 1/5 more white balls than yellow balls.. Can someone please explain the logic/steps for the preceding bold statement as to how it would be 1/5 more white balls?

Thanks in advance.


Received White : Yellow = 6 : 5
This difference of 1 in ratio terms is actually equal to 30 balls (since 30 extra white balls were sent). This means our multiplier is 30.

Hence, no of yellow balls ordered = 5 * 30 = 150 = Number of white balls ordered.
Total no of balls ordered = 150 + 150 = 300

Answer (D)
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Re: A sporting goods store ordered an equal number of white and yellow ten [#permalink]
28 Mar 2023, 22:42
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