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

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by BTGmoderatorLU » Wed Feb 14, 2018 6:05 am
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

The OA is D.

The price of each cake is $x.

The next week she reduces the price by 20 percent, 0.8x$.

I can say that the number of cakes is y.

then, x*y = 320 but the next week will be, 0.8x * (y+2) = 320, Now from those two equations I can get the value of x, right?

Experts, any suggestion about this PS question? Thanks in advance.
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by ErikaPrepScholar » Wed Feb 14, 2018 6:48 am
This is an effective way to solve the problem. We have the same number of distinct equations as variables (2), so we should be able to solve for the variables.

Expanding the second equation gives$$0.8xy+1.6x=320$$Then plugging in 320 for xy gives$$0.8\left(320\right)+1.6x=320$$ Then solving for x gives 40

Plugging x into the first equation (since it's easier) gives$$40y=320$$ Then solving for y gives 8. So the correct answer is D.
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by [email protected] » Wed Feb 14, 2018 3:09 pm
Hi LUANDATO,

We're told that a baker charges X dollars for a birthday cake and that 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 2 MORE cakes to earn the same amount of revenue. We're asked for the number of cakes that she intends to sell next week. This question can be solved by TESTing THE ANSWERS.

Since the answer choices are 'nice' round numbers - and the total money earned is $320 when we sell N cakes AND when we sell (N+2) cakes, we're almost certainly looking for a number for N and (N+2) that BOTH evenly divide into 320. Answer D would give us N=8 and (N+2) = 10 - and both of those values evenly divide into 320, so we'll TEST that Answer first.

Answer D = 8 cakes
IF.... there are 8 cakes, then each cake sells for $320/8 = $40
Reducing the cost/cake by 20% would turn the cost of a cake into $40 - (.2)($40) = $40 - $8 = $32
At $32/cake, it would take $320/$32 = 10 cakes to make the same amount of money.
The difference in cakes here (8 vs. 10) is an exact match for everything we were told, so this MUST be the answer.

Final Answer: D

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Rich
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by Scott@TargetTestPrep » Thu Feb 15, 2018 10:34 am
LUANDATO 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

Answer: D

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