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On Christmas, Susanne bought a few flowers for $1.

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On Christmas, Susanne bought a few flowers for $1.  [#permalink]

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New post 21 Apr 2019, 06:04
2
2
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A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

35% (03:24) correct 65% (03:14) wrong based on 23 sessions

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On Christmas, Susanne bought a few flowers for $1. The flower vendor was running a special Christmas offer which Susanne did not opt for. Had she opted for the offer, she would have spent $2 but got 30 more flowers and saved 60 cents per each dozen of flowers. How many flowers did she buy?

A. 40
B. 30
C. 20
D. 15
E. 10

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Re: On Christmas, Susanne bought a few flowers for $1.  [#permalink]

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New post 21 Apr 2019, 06:41
5
Let Susanne bought x flowers.
The total cost of x flowers = $1 = 100 cents
Price of 1 flower = 100/x
Price of 1 dozen (12 units) flowers = 1200/x

Accordingly to the Chrismas offer.
The total cost of (x + 30) flowers = $2 = 200 cents
Price of 1 flower = 200/(x +30)
Price of 1 dozen (12 units) flowers = 2400/(x +30)

Doing so, Susanne saved 60 cents per each dozen of flowers
1200/x - 2400/(x +30) = 60
20/x - 40/(x +30) = 1
1/x - 2/(x + 30) = 1/20
x^2 + 50 x - 600 = 0
x = 10 or -60 (ignore)

Therefore, Susanne bought 10 flowers. Hence, the correct answer is option E. 10

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On Christmas, Susanne bought a few flowers for $1.  [#permalink]

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New post 21 Apr 2019, 14:03
In order to save money, the number of flowers bought has to be less than 30 flowers.

We can eliminate A & B.

C) \(\frac{100c}{20} = 5c\) \(5c*12 = 60c\) So 20 + 30 = 50 flowers \(\frac{200c}{50} = 4c\) So \(4c*12 = 60c\) No change, eliminate.

D) \(\frac{100c}{15} = 6.6c\) \(6.6c*12 = 80c\) So 15 + 30 = 45 flowers \(\frac{200c}{45} = 4.5c\) So \(4.5c*12 = 54c\) \(80 - 54 = 26c\) ...Eliminate

E) \(\frac{100c}{10} = 10c\) \(10c*12 = 120c\) So 10 + 30 = 40 flowers \(\frac{200c}{40} = 5c\) \(5c*12 = 60c\) So \(120- 60 = 60c\) ... Correct

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Re: On Christmas, Susanne bought a few flowers for $1.  [#permalink]

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New post 23 Apr 2019, 05:02
Let she bought x flowers in 1$.
Discount is 60/12=5 cents/flower.
In case if she had bought x+30 flowers (2nd case) then she would have saved
30×5=150 cents =1.5 $
If w/o discount she had bought x+30 flowers the price would have been
1$+1.5$=2.5$
But with discount she saved 0.5$ or 50 cents on x flowers so
x= 50cents saved/ discount rate(5cents)
x=50/5=10 flowers

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Re: On Christmas, Susanne bought a few flowers for $1.   [#permalink] 23 Apr 2019, 05:02
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