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04 Jan 2018, 22:45
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Difficulty:

45% (medium)

Question Stats:

75% (02:15) correct 25% (02:29) wrong based on 76 sessions

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A rural country store's annual sales of bottled soda totaled $75,000 last year. This year the price of a bottle of soda was 30 percent higher than last year but the number of bottles sold was 30 percent lower. What is value of store's total sales of bottled soda for this year? A.$82,500
B. $75,000 C.$72,750
D. $68,250 E.$38,750

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Re: A rural country store's annual sales of bottled soda totaled $75,000 [#permalink] ### Show Tags 05 Jan 2018, 00:05 Bunuel wrote: A rural country store's annual sales of bottled soda totaled$75,000 last year. This year the price of a bottle of soda was 30 percent higher than last year but the number of bottles sold was 30 percent lower. What is value of store's total sales of bottled soda for this year?

A. $82,500 B.$75,000
C. $72,750 D.$68,250
E. $38,750 Let number of bottles be n, cost per bottle be x. The total annual sales of bottled soda last year was$75000(n*x)
Assume n=1000 and x=75
P.S Take number that are easy to work with, to make calculations easier

This year the number of bottles sold was 30% lower, making n = 700(0.7*1000)
Similarly the cost per bottle was 30% higher, making the cost x = 75*1.3 = 97.5
Therefore, the value of the total sales is 700*97.5 = 975*70 = 68250(Option D)
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A rural country store's annual sales of bottled soda totaled $75,000 [#permalink] ### Show Tags 05 Jan 2018, 08:00 1 1 Bunuel wrote: A rural country store's annual sales of bottled soda totaled$75,000 last year. This year the price of a bottle of soda was 30 percent higher than last year but the number of bottles sold was 30 percent lower. What is value of store's total sales of bottled soda for this year?

A. $82,500 B.$75,000
C. $72,750 D.$68,250
E. $38,750 Answer B is the trap. When each factor in a product has a percent increase and/or decrease, find each factor's multiplier, then multiply the multipliers. That's the overall percent change. (Price per bottle, P)(# of bottles, N) =$75,000

Price increases 30 percent = 1.3
Number of bottles decreases by 30 percent = .70

(1.3P)(.70N) = (?) * $75,000 Multiply the multipliers: (1.3)(.7) = .91, thus (1.3P)(.7N) = .91 ($75,000)

The revenue is 91 percent of what it was.

(.91)($750) =$682.50
=> $68,250, OR Split the multiplier: $$\frac{90}{100}=\frac{9}{10} * 750 = 675$$ $$\frac{1}{100} * 750 = 7.5$$ $$675 + 7.5 = 682.50$$ => $$68,250$$ Answer D _________________ Life’s like a movie. Write your own ending. Kermit the Frog Intern Joined: 12 Oct 2017 Posts: 4 Re: A rural country store's annual sales of bottled soda totaled$75,000  [#permalink]

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15 Jan 2018, 23:46
P=price, Q=quantity
Price*quantity=75000
Price percentage increase=30%
Quantity percentage decrease=30%
Net percentage increase/decrease on PQ= 30%-30%-(30%*30%)/100..........(effective percentage formula)
Net percentage effect= -9%(or 9% decrease).Therefore PQdecrease by 9%
Now PQ on 100%=75000
Then PQ on 91%=x
Cross multiply to get x=75000*91/100=68250.
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Re: A rural country store's annual sales of bottled soda totaled $75,000 [#permalink] ### Show Tags 15 Jan 2018, 23:54 Approximation technique maybe mightily helpful in this question. We know that a cycle of successive %age increase-decrease of a quantity results in the overall decrease. Thus, options A and B are gone. Now, %age increase in price of soda bottle = 30% --> 1.3x Similarly, quantity of soda bottles sold = 30% less than last year --> 0.7y Multiplying the above two equations, we get (1.3)(0.7)xy = 0.91xy. We know that the sales for last year was$75,000. Using this in the above equation, we get 0.91(75,000). We know that 90% of 750 is 675, so the closest value to it is our answer.

Thus, D.
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A rural country store's annual sales of bottled soda totaled $75,000 [#permalink] ### Show Tags 16 Jan 2018, 11:00 Bunuel wrote: A rural country store's annual sales of bottled soda totaled$75,000 last year. This year the price of a bottle of soda was 30 percent higher than last year but the number of bottles sold was 30 percent lower. What is value of store's total sales of bottled soda for this year?

A. $82,500 B.$75,000
C. $72,750 D.$68,250
E. $38,750 Hi Bunuel, here is my solution. can you please advice if i made a mistake ? :? i got correct answer but i think i mixed up variables or not :? :) Thanks! Let total number of bottles sold last year be n Total value received 75 000 Then cost of each bottle $$\frac{75000}{n}$$ = x (first equation) where x is cost of each bottle Let total value of bottles sold this year be R Total number of bottles is n Total number of bottles sold this year decreased by 30 % --- > n-0.30n The cost of each bottle increased by 30% ---- > X(1.3) So here we have second equation X(1.3) * (n-0.30n) = R Now plug in first equation into the second one: $$\frac{75 000(1.3)}{n}$$ * $$(n-0.30n) = R$$ $$\frac{97 500}{n}$$* $$(n-0.30n) = R$$ $$\frac{(97 500n – 29 250 n)}{n}$$ =$$R$$ $$\frac{68 250n}{n}$$ = $$R$$ P.S niks18, perhaps you can explain Bunuel is kinda busy:) Retired Moderator Joined: 25 Feb 2013 Posts: 1220 Location: India GPA: 3.82 Re: A rural country store's annual sales of bottled soda totaled$75,000  [#permalink]

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17 Jan 2018, 01:59
1
1
dave13 wrote:
Bunuel wrote:
A rural country store's annual sales of bottled soda totaled $75,000 last year. This year the price of a bottle of soda was 30 percent higher than last year but the number of bottles sold was 30 percent lower. What is value of store's total sales of bottled soda for this year? A.$82,500
B. $75,000 C.$72,750
D. $68,250 E.$38,750

Hi Bunuel,

here is my solution. can you please advice if i made a mistake ? :? i got correct answer but i think i mixed up variables or not :? :) Thanks!

Let total number of bottles sold last year be n
Then cost of each bottle $$\frac{75000}{n}$$ = x (first equation)
where x is cost of each bottle

Let total value of bottles sold this year be R
Total number of bottles is n
Total number of bottles sold this year decreased by 30 %
--- > n-0.30n
The cost of each bottle increased by 30% ---- >
X(1.3)

So here we have second equation X(1.3) * (n-0.30n) = R

Now plug in first equation into the second one:

$$\frac{75 000(1.3)}{n}$$ * $$(n-0.30n) = R$$

$$\frac{97 500}{n}$$* $$(n-0.30n) = R$$

$$\frac{(97 500n – 29 250 n)}{n}$$ =$$R$$

$$\frac{68 250n}{n}$$ = $$R$$

P.S niks18, perhaps you can explain Bunuel is kinda busy:)

Hi dave13

Yes your method is correct. however you can use a simple approach here -

if $$n$$ is the initial number of bottles and $$r$$ is the initial rate per bottle, then we have

$$n*r=75000$$

Now after $$30$$% increase in rate and $$30$$% reduction in number of bottles we will have new revenue $$R_1$$, as -

$$R_1=0.7n*1.3r=0.91nr=0.91*75000=68250$$