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Red roses cost $ 9 and yellow roses costs $14

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ajithkumar
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Red roses cost $ 9 and yellow roses costs $14 [#permalink] New post   11 Apr 2014, 09:23
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67% (03:02) correct 33% (02:59) wrong based on 224 sessions
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Richard bought a number of red roses and yellow roses on February 14th. Each red rose costs $9, and each yellow rose costs $14. If Richard spent a total of exactly $220, how many roses did Richard buy?

(A) 16
(B) 17
(C) 19
(D) 20
(E) 21
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D
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Bunuel
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Re: Red roses cost $ 9 and yellow roses costs $14 [#permalink] New post   11 Apr 2014, 09:46
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ajithkumar wrote:
Richard bought a number of red roses and yellow roses on February 14th. Each red rose costs $9, and each yellow rose costs $14. If Richard spent a total of exactly $220, how many roses did Richard buy?

(A) 16
(B) 17
(C) 19
(D) 20
(E) 21


Say Richard bought total of \(x\) roses, out of which \(r\) were red roses. So, the number of yellow roses were \(x-r\).

\(9r + 14(x-r)= 220\);

\(14x-5r=220\);

\(14x=5(44+r)\) --> \(x\) is a multiple of 5. Only option D satisfies that.

Answer: D.
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Re: Red roses cost $ 9 and yellow roses costs $14 [#permalink] New post   29 Jun 2019, 11:38
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This problem can also be solved by allegation method.

Total = 220
n=? (Choose a smart number that clearly divides 220) 20 is the only such number.
Combined Average= 220/20=11

Now the allegation:

9=======14
====11====
3========2

IS THE ASSUMED NUMBER (20) is clearly divisible by (3+2) =5? YES.
That mean, this 20 can be allocated to $9 &$14 groups in 3:2 ratio (12&8)

So, total number is 20.

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Rafaelurlich
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Red roses cost $ 9 and yellow roses costs $14 [#permalink] New post   29 Jun 2019, 10:54
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to start, let's imagine 10 Red roses and 10 Yellow roses. That would be 10x9 + 10x14 = 230. However, the total cost was 220. So we need to lower our calculated cost by 10, which can be done by adding 2 Red roses and reducing 2 Yellow Roses: +2*9 - 2*14 = -10.

This way, we would have 12 Red roses and 8 Yellow roses: total 20 roses.

Thanks!
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ind23
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Re: Red roses cost $ 9 and yellow roses costs $14 [#permalink] New post   11 Apr 2014, 12:57
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Bunuel wrote:
ajithkumar wrote:
Richard bought a number of red roses and yellow roses on February 14th. Each red rose costs $9, and each yellow rose costs $14. If Richard spent a total of exactly $220, how many roses did Richard buy?

(A) 16
(B) 17
(C) 19
(D) 20
(E) 21


Say Richard bought total of \(x\) roses, out of which \(r\) were red roses. So, the number of yellow roses were \(x-r\).

\(9r + 14(x-r)= 220\);

\(14x-5r=220\);

\(14x=5(44+r)\) --> \(x\) is a multiple of 5. Only option D satisfies that.

Answer: D.



An another method could be:

lets x be the min (no of red roses, no of yellow roses)

so x number of both red and yellow roses are bought

so the price of these 2x roses would be (9+14)*x = 23x

Now as the total price is 220, the highest integer value for x could be 9 and remainder is 13
given 13 is neither a multiple of 9 or 14, we check for x = 8, remainder = 23+13 = 36 = 4*9

hence the total number of roses = x+x+4 = 8+8+4 = 20

Answer D.

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Re: Red roses cost $ 9 and yellow roses costs $14 [#permalink] New post   12 Apr 2014, 22:33
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Bunuel wrote:
ajithkumar wrote:
Richard bought a number of red roses and yellow roses on February 14th. Each red rose costs $9, and each yellow rose costs $14. If Richard spent a total of exactly $220, how many roses did Richard buy?

(A) 16
(B) 17
(C) 19
(D) 20
(E) 21


Say Richard bought total of \(x\) roses, out of which \(r\) were red roses. So, the number of yellow roses were \(x-r\).

\(9r + 14(x-r)= 220\);

\(14x-5r=220\);

\(14x=5(44+r)\) --> \(x\) is a multiple of 5. Only option D satisfies that.

Answer: D.


I find this approach a bit easier. This will be better even when there are two options that are multiples of 5.

The only possible combo is 12+8 = 20

So answer D
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Maxcromea
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Red roses cost $ 9 and yellow roses costs $14 [#permalink] New post   29 Jun 2019, 11:40
Have used such logic - first buyed only expensive roses and check overbudgeting for each answer (e.g. for first answer it’s 14*16 - 220 = 4). this overbudgeting must be compensated by changing of expensive rose by cheaper (5$ for each change). So overbudgeted amount must be divisible by 5 - answer D
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Re: Red roses cost $ 9 and yellow roses costs $14 [#permalink] New post   04 Dec 2023, 02:48
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Re: Red roses cost $ 9 and yellow roses costs $14 [#permalink]
04 Dec 2023, 02:48
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