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# A baker charges x dollars for a birthday cake. Next week, she intends

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Math Expert
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A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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15 May 2015, 04:18
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Difficulty:

55% (hard)

Question Stats:

65% (02:10) correct 35% (02:29) wrong based on 187 sessions

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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

Kudos for a correct solution.

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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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15 May 2015, 09:36
4
1
Bunuel wrote:
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

Kudos for a correct solution.

Price of each cake= \$x
No of cakes=y
Now, x*y=320
And 0.8x*(y+2)=320

Solving the two equations,
xy=320
And, 0.8xy+1.6x=320
x=40

Put the value of xy=320,
x=40, y=8
##### General Discussion
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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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15 May 2015, 10:11
1
Assume number of cake sale = n, Price/cake = x

x*n=320;
Reduced cake price= 0.8 *x, then number will increase by two so (n+2) => (n+2)*0.8x=320

Equating above both equation, x*n=(n+2)*0.8x ; solving this equation we get n=8

Thanks,
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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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15 May 2015, 10:39
2
Let number of cake be n and cost of a cake be x

hence, nx=320.......(1)
Now, (n+2)*0.8x=320
thus, x=40
n=8
(D)
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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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15 May 2015, 15:45
2
1
Hi All,

Many Test Takers would take an Algebraic approach with this question (which is fine). Sine the answers are NUMBERS, and we're asked for the number of cakes the baker intends to sell, we can TEST THE ANSWERS.

We're told that by selling cakes at X dollars/cake, a baker will make \$320.
Reducing the price by 20% and selling 2 MORE cakes will also make her \$320.

We're asked for the original number of cakes that the baker intends to sell.

\$320 is a rather interesting number. Based on the answer choices, we're almost certainly dealing with integer values for the number of cakes AND the price per cake. As such, 6 is probably NOT going to be part of the solution (either as 4 and 6 cakes or as 6 and 8 cakes). As such, we can avoid Answers B and C....

Let's TEST ANSWER D: 8 cakes

IF....
Original cakes = 8
8(X) = \$320, so X = \$40/cake
20% off = \$8 off = 40-8 = \$32/cake
+2 more cakes = 8+2 = 10 cakes
10(32) = \$320

This is an exact MATCH for what we were told, so this MUST be the answer.

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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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15 May 2015, 16:02
1
let n=the number of birthday cake
so the number of cake will be sell next week=n+2
x*n=320
80%x*(n+2)=320
4/5x(n+2)=n*x
4/5(n+2)=n
4/5n+8/5=n
8/5=n-4/5n
8/5=n/5
5n=40
n=8
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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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15 May 2015, 21:07
1
1
Bunuel wrote:
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
[/i]

Ans: D

Solution: Equation based question : if price is reduced by 20% then selling price= 256
now she has to sell two more = n+2
now
256*(n+2)=360*n
n=8
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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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15 May 2015, 22:34
1
Let No of cakes = C
Price of a cake = X

So C*X=320 --------- (1)

If price of a cake is decreased by 20 %, New price will be 0.80 of X

So 0.80 X ( C+2 ) = 320 ------------ (2)

Solving (1) and (2) we get

X= 40 and C = 8.

Hence (D. 8) is the correct answer
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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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16 May 2015, 01:18
1
I think the question is asking us to find out N+2 as we need to find out the number of cakes she needs to sell next week .... Thus it must be 8+2 = 10

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A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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16 May 2015, 04:05
3
Bunuel wrote:
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

Kudos for a correct solution.

THIS QUESTION CAN BE SOLVED WITHOUT USING 320\$ OR x \$--- Data Sufficiency point of view

Price is reduced by 20% and therefore, to earn the same revenue she must increase the quantity sold by 25%. Thus, from the question, 25% of original quantity = 2. Thus total original quantity = 2*4 = 8 Option D

Alternatively: revenue = price * quantity. Let price = quantity = 10
Thus, revenue = 100
New price = 8 and let new quantity be q
Since revenue is constant, we have 100= 8* q
Thus q = 12.5
Change in quantity = 12.5 - 10 = 2.5
Now when change in quantity is 2.5, original quantity is 10
Thus when change is quantity is 2 (as per the question), required original quantity = (10/2.5)*2 = 8 Option D

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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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16 May 2015, 08:57
sagarsingh wrote:
Bunuel wrote:
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

Kudos for a correct solution.

THIS QUESTION CAN BE SOLVED WITHOUT USING 320\$ OR x \$--- Data Sufficiency point of view

Price is reduced by 20% and therefore, to earn the same revenue she must increase the quantity sold by 25%. Thus, from the question, 25% of original quantity = 2. Thus total original quantity = 2*4 = 8 Option D

Alternatively: revenue = price * quantity. Let price = quantity = 10
Thus, revenue = 100
New price = 8 and let new quantity be q
Since revenue is constant, we have 100= 8* q
Thus q = 12.5
Change in quantity = 12.5 - 10 = 2.5
Now when change in quantity is 2.5, original quantity is 10
Thus when change is quantity is 2 (as per the question), required original quantity = (10/2.5)*2 = 8 Option D

Wow! +1 to you! Thanks for the (1st) solution!
I know the concept but didn't use it here!
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Posts: 58427
Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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18 May 2015, 06:52
Bunuel wrote:
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

Kudos for a correct solution.

OFFICIAL SOLUTION:

Reducing the price by 20%, so multiplying the price by 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 10/8 times as many cakes. Thus, we are basically told that (the number of cakes)*10/8 = (the number of cakes) + 2, which means that (the number of cakes) = 8.

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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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27 Nov 2016, 17:40
Setup

Original
--------
Price: x
Quantity: y
Revenue: 320

Change
-------
Price: 0.80x
Quantity: y+2
Revenue: 320

0.80x(y+2)=320
0.80xy+1.6x=320
0.80(320)+1.6x=320
256+1.6x=320
1.6x=64
x=40 --> Plug back into original equation to find quantity (y)

40(y)=320
y=8

D.
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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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15 Feb 2018, 11:28
Bunuel wrote:
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

We can create the equations in which c = number of cakes she intends to sell next week:

xc = 320

x = 320/c

and

(0.8x)(c + 2) = 320

0.8xc + 1.6x = 320

Substituting we have:

0.8(320) + 1.6(320/c) = 320

256 + 512/c = 320

512/c = 64

512 = 64c

c =512/64 = 8

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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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14 Mar 2018, 02:03
Hi Guys,

I'm really having problems with Word Problems in general...I've been going through the GMAT Club questions systematically (topic by topic) and even though they've been tough I've generally understood the explanations as there seem to be fundamental rules underlying each topic.

However, with the Word Problems segment I'm averaging 4/10 per 10 question quiz...and finding it difficult to translate the questions...this question is a case in point...

How do you know that it is x(selling price of cake) times c (number of cakes) = 320

What is the rationale behind it?

Why for instance is it not x/c=320?

Is there a resource I can use that provides a systematic approach to answering Word Problems?

Thanks,

Tosin
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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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19 Mar 2018, 08:46
ttaiwo wrote:
Hi Guys,

I'm really having problems with Word Problems in general...I've been going through the GMAT Club questions systematically (topic by topic) and even though they've been tough I've generally understood the explanations as there seem to be fundamental rules underlying each topic.

However, with the Word Problems segment I'm averaging 4/10 per 10 question quiz...and finding it difficult to translate the questions...this question is a case in point...

How do you know that it is x(selling price of cake) times c (number of cakes) = 320

What is the rationale behind it?

Why for instance is it not x/c=320?

Is there a resource I can use that provides a systematic approach to answering Word Problems?

Thanks,

Tosin

Hi Tosin,

How do you know that it is x(selling price of cake) times c (number of cakes) = 320
Consider this example, you are selling 8 apples (c) and each apple for \$10 (x).
Now, how will you calculate the money earned/made by selling 8 apples --> it will be \$10(x)* 8 apples(c) =80.

So, there is no such complex rationale behind this x*c=320.
And, x/c does not make sense here.
Resource: gmat club math book should help.

Hope this helps you!!

~Cheers !!
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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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22 Aug 2018, 05:28
HI VeritasKarishma, Bunuel, niks18, generis, pushpitkc

One Quick doubt How many cakes does she intend to sell next week?

Current number of cakes she intend to sell is 8

But if she reduces the price by 20 percent then she has to sell 8+2?

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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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22 Aug 2018, 06:17
1
Bunuel wrote:
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

Kudos for a correct solution.

Hey NandishSS

We are talking about a time, which was one week ago.

So, when the author asks, how many cakes does she intend to sell next week, we are
essentially talking about the same time. For more clarification see the highlighted part
of the question which refers to the next week. So, in essence, both the times are the same.

Hope I clarified your doubt and not confused you further
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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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22 Aug 2018, 06:34
pushpitkc wrote:
Bunuel wrote:
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

Kudos for a correct solution.

Hey NandishSS

We are talking about a time, which was one week ago.

So, when the author asks, how many cakes does she intend to sell next week, we are
essentially talking about the same time. For more clarification see the highlighted part
of the question which refers to the next week. So, in essence, both the times are the same.

Hope I clarified your doubt and not confused you further

Got It now

Thanks a lot
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Re: A baker charges x dollars for a birthday cake. Next week, she intends  [#permalink]

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15 Oct 2018, 01:48
Let the price be 100.
Discounted price-80
x be the number of cakes to be sold
100x=80(x+2)
x=8
Did I miss something?
Re: A baker charges x dollars for a birthday cake. Next week, she intends   [#permalink] 15 Oct 2018, 01:48

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