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M31-08

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M31-08 [#permalink]

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A baker charges \(x\) dollars for a birthday cake. Next week, she intends to earn 320 dollars selling cakes. If she were to reduce the price of the cake by 20 percent, she would have to sell two more cakes to earn the same amount of revenue. How many cakes does she intend to sell next week?

A. 2
B. 4
C. 6
D. 8
E. 10
[Reveal] Spoiler: OA

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Official Solution:

A baker charges \(x\) dollars for a birthday cake. Next week, she intends to earn 320 dollars selling cakes. If she were to reduce the price of the cake by 20 percent, she would have to sell two more cakes to earn the same amount of revenue. How many cakes does she intend to sell next week?

A. 2
B. 4
C. 6
D. 8
E. 10


Reducing the price by 20%, so multiplying the price by \(\frac{8}{10}\), results in selling two more cakes to earn the same amount of revenue. So, in this scenario, to get the same revenue, the baker must sell \(\frac{10}{8}\) times as many cakes. Thus, we are basically told that \((the \ number \ of \ cakes)*\frac{10}{8} = (the \ number \ of \ cakes) + 2\), which means that (the number of cakes) = 8.


Answer: D
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Re: M31-08 [#permalink]

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There is ambiguity in the question. You say If she were to reduce the price of the cake by 20 percent, she would have to sell two more cakes to earn the same amount of revenue How many cakes does she intend to sell next week?

She intends to sell the cakes with x dollars (Original price) or .8x (reduced price)?
If it is the earlier then the answer is 8 otherwise is 10

Please clarify.

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Re: M31-08 [#permalink]

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New post 07 Apr 2016, 14:14
Hi Buñuel,

I tried solving this question by substituing one of the variables but I couldn´t solve the equations. Why is this? Please see below:
p=initial price
c= number of cakes

320=pc
320= .8p( c+2)

c=320/p

320= .8p(320/p+2)

Why solving the equations does not work to solve the problem?

Thanks,
Ang

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Re M31-08 [#permalink]

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New post 25 Jun 2016, 02:04
I think this is a high-quality question and I don't agree with the explanation. you have answered number of cakes as 8, But the number of cakes to be sold next week are (8+2)=10

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Navinder wrote:
I think this is a high-quality question and I don't agree with the explanation. you have answered number of cakes as 8, But the number of cakes to be sold next week are (8+2)=10


Check here: a-baker-charges-x-dollars-for-a-birthday-cake-next-week-she-intends-198284.html

Hope it helps.
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Re: M31-08 [#permalink]

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New post 19 Oct 2016, 19:49
I see you have posted the link to the discussion, but it does not address the ambiguity in the question. The number of cakes was solved to be 8. But the number she intends to sell next week is 8+2 = 10. Please correct the answer here

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Re: M31-08 [#permalink]

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New post 18 Dec 2016, 22:51
HI,

IS THE ANSWER 10.?

PLEASE HELP.

THANKS

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New post 11 Jan 2017, 03:44
satyakrishna warpedhobbit
The right answer is 8.
The question asks how many cakes she intended to sale to earn 320$.
The second information says that she need to sell 2 more cakes if and only if she would reduce the price by 20 % ...

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Re M31-08 [#permalink]

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New post 25 Jan 2017, 23:18
I think this is a high-quality question and I don't agree with the explanation. She would have to sell 8+2=10 cakes next week.

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New post 25 Jan 2017, 23:24
rohit789 wrote:
I think this is a high-quality question and I don't agree with the explanation. She would have to sell 8+2=10 cakes next week.


Did you see that the question asks "how much she intended to sell" and not how much she has to sell, if she would reduce the price by 20% ?

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Re: M31-08 [#permalink]

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New post 25 Jan 2017, 23:50
Yeah, also I thought that she was gonna reduce the price and sell. I think the trick is "she were"

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Re: M31-08 [#permalink]

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New post 24 Nov 2017, 21:31
Revenue = Price per cake * Number of cakes
Let T be the number of cakes being sold

So, x * T = .8x * (T+2)
=> T = 8
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Re: M31-08   [#permalink] 24 Nov 2017, 21:31
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