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A class collects $50 to buy flowers for a classmate who is in the hosp

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A class collects $50 to buy flowers for a classmate who is in the hosp  [#permalink]

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New post 16 Mar 2019, 21:42
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Difficulty:

  55% (hard)

Question Stats:

63% (02:04) correct 38% (01:50) wrong based on 32 sessions

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A class collects $50 to buy flowers for a classmate who is in the hospital. Roses cost $3 each, and carnations cost $2 each. No other flowers are to be used. How many different bouquets could be purchased for exactly $50?

(A) 1 (B) 7 (C) 9 (D) 16 (E) 17
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Re: A class collects $50 to buy flowers for a classmate who is in the hosp  [#permalink]

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New post 16 Mar 2019, 22:14
1
ImO C .

He can by the roses in the following sequence.

0 rose and rest carmations

6$ roses and rest carnation
12$ roses and rest ...
18$ roses and rest ..
24 $ roese and rest

similarly , he can buy roses in such a way that the leftover amount ( after buying roses) should be divisible by 2.

we get 9 such optiina


award kudos if helpful

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A class collects $50 to buy flowers for a classmate who is in the hosp  [#permalink]

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New post 17 Mar 2019, 11:24
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Rubina11 wrote:
A class collects $50 to buy flowers for a classmate who is in the hospital. Roses cost $3 each, and carnations cost $2 each. No other flowers are to be used. How many different bouquets could be purchased for exactly $50?

(A) 1 (B) 7 (C) 9 (D) 16 (E) 17




As $50 is divisible by $2 so let's start with all C flowers.

25C * $2= $50
With $50, we can have maximum 16R ($3*16= $48) + 1C ($2*1=$2)
Gradually, ............................... 14R ($3*14= $42) + 4C ($2*4=$8)
12R ($3*12= $36) + 7C ($2*7=$14)
10R ($3*10= $30) + 10C ($2*10=$20)
8R ($3*8= $24) + 13C ($2*13=$26)
6R ($3*6= $18) + 16C ($2*16=$32)
4R ($3*4= $12) + 19C ($2*19=$38)
2R ($3*2= $6) + 22C ($2*22=$44) ; TOTAL 9 Possibilities.

Any shortcut or easier way to solve this kinda problem ? Thanks
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Re: A class collects $50 to buy flowers for a classmate who is in the hosp  [#permalink]

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New post 18 Mar 2019, 04:03
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hi TRINA6
The total number of dollars spent is the even number 50,
so the number of roses purchased must also be even.
In addition, the number of roses purchased cannot exceed 50/3
Therefore the number of roses purchased must be one of the even integers between 0 and 16, inclusive. This gives 9 possibilities for the
number of roses purchased, and consequently 9 possibilities for the number of bouquets.
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Re: A class collects $50 to buy flowers for a classmate who is in the hosp  [#permalink]

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New post 19 Mar 2019, 03:10
1
Rubina11 wrote:
hi TRINA6
The total number of dollars spent is the even number 50,
so the number of roses purchased must also be even.
In addition, the number of roses purchased cannot exceed 50/3
Therefore the number of roses purchased must be one of the even integers between 0 and 16, inclusive. This gives 9 possibilities for the
number of roses purchased, and consequently 9 possibilities for the number of bouquets.





Make sense, thanks Rubina11 :)
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Re: A class collects $50 to buy flowers for a classmate who is in the hosp   [#permalink] 19 Mar 2019, 03:10
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A class collects $50 to buy flowers for a classmate who is in the hosp

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