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

Question

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.

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

KS15 · Accepted Answer

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
Answer =D

Bunuel · Answer

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.

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

Reducing the price by 20% is equivalent to multiplying the price by  \frac{8}{10} . In this scenario, to achieve the same revenue, the baker must sell  \frac{10}{8}  times as many cakes. Essentially, we are told that  (	ext{number of cakes}) * \frac{10}{8} = (	ext{number of cakes}) + 2 , which implies that the number of cakes is 8.
 
Another way to look at this is by noting that when the price is reduced by 20%, it becomes 4/5th of the original price. To earn the same revenue, she must increase the quantity sold by 25% (the revenue must increase by 5/4 times to compensate for the reduction in price to 4/5th). From the question, we know that 25% of the original quantity equals 2. Thus, the total original quantity is 2 * 4 = 8.

Answer: D

lipsi18 · Answer

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

Hence answer is D

Thanks,

masoomdon · Answer

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)

EMPOWERgmatRichC · Answer

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.

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

23a2012 · Answer

The answer is D
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

D3N0 · Answer

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

cutegirlsimran · Answer

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

Udai · Answer

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

Hence Answer should be E

sagarsir · Answer

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 KUDOS PLEASE!!

ScottTargetTestPrep · Answer

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

Answer: D

bumpbot · Answer

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

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