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A convenience store currently stocks 48 bottles of mineral water. The

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A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?

(A) 10
(B) 20
(C) 30
(D) 32
(E) 34
[Reveal] Spoiler: OA
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New post 27 Jun 2007, 17:55
dred wrote:
A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?
10
20
30
32
34


D.

20 p + 40 (1-p) = 35
p = 1/4
so 20 oz = 12

12 x 20 / (12+x) + 40x / (12+x) = 25

x = 4
so 32 bottles with 40 oz should be sold.
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32

Here is how I got it:

Average is 35 ounces
x is # of 20 ounce bottles
y is # of 40 ounce bottles

20x+40y/x+y = 35
solve to get y=3x

x+y=48 bottles
x=12, y=36

20x+40z/x+z=25

plug x=12 and solve for z, we get z = 4

So, y-z is # of bottles sold i.e 36-4 = 32
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A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?

(A) 10
(B) 20
(C) 30
(D) 32
(E) 34

Last edited by Bunuel on 27 Sep 2014, 12:47, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink]

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GGUY wrote:
Taken From MGMAT # 3

A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?

(A) 10
(B) 20
(C) 30
(D) 32
(E) 34

Please Explain

D

20x + 40y = 35*48

20x + 40 (y-t) = 25*(48-t)
20x + 40y -40t = 25*48 - 25t
35*48 -40t = 25*48 -25t
t =32
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New post 22 Jan 2008, 13:10
sondenso wrote:
GGUY wrote:
Taken From MGMAT # 3
A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?

(A) 10
(B) 20
(C) 30
(D) 32
(E) 34

Please Explain

D

20x + 40y = 35*48

20x + 40 (y-t) = 25*(48-t)
20x + 40y -40t = 25*48 - 25t
35*48 -40t = 25*48 -25t
t =32
Nice, OA= D.

My approach was to find how many bottles of 40 need to remain in order to have 25 Av:

(1) 12*20+40*t = 25* (t+12)
(2) t=4
(3) we found 12 bt of 20 ounce and 36 of 40 ounce so 36-4=32

any more takers?
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hey can any1 plz tell me ..
if ques says that no 20 ounce bottles are sold..
then y r we considering "20*12" while calculating the new ratio..
wats the meaning and the use of that line above.." no 20 ounce bottles are sold"
y can`t we directly put 0 bottles for 20 ounces..

y can`t we go directly for ..

25=(20(0)+40(x))/x..

confused..:(
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shreygupta3192 wrote:
A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?

(A) 10
(B) 20
(C) 30
(D) 32
(E) 34

hey can any1 plz tell me ..
if ques says that no 20 ounce bottles are sold..
then y r we considering "20*12" while calculating the new ratio..
wats the meaning and the use of that line above.." no 20 ounce bottles are sold"
y can`t we directly put 0 bottles for 20 ounces..

y can`t we go directly for ..

25=(20(0)+40(x))/x..

confused..:(


No. The question asks about the average weight of bottles which are not sold.

A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?

(A) 10
(B) 20
(C) 30
(D) 32
(E) 34

The current average of 20 (35 - 15) and 40-ounce (40 - 5) bottles is 35, thus there must be 3 times as many 40-ounce bottles as 20-ounce bottles. Since there are total of 48 bottles, then there must be 12 20-ounce bottles and 36 40-ounce bottles.

Now, we need to sell ONLY 40-ounce bottles so that the average to become 25. Same way, 25 is 5 away from 20 and 15 away from 40, so after selling some number of 40-ounce bottles, there must be 3 times as many 20-ounce bottles as 40-ounce bottles. So, there must be 12 20-ounce bottles and 12/3 = 4 40-ounce bottles.

Therefore, 36 - 4 = 32 40-ounce bottles must be sold.

Answer: D.

Hope it's clear.
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hi thanx for ur valuable answer but i`ll be glad if u could put it algebrically...that will be more easier for me to understand.

also, plz tell me wat is the point of "20 ounces bottles not sold" ... y r we still considering that while calculating the new ratio..it should be 0 ..huh..
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New post 29 Sep 2014, 06:12
shreygupta3192 wrote:
hi thanx for ur valuable answer but i`ll be glad if u could put it algebrically...that will be more easier for me to understand.

also, plz tell me wat is the point of "20 ounces bottles not sold" ... y r we still considering that while calculating the new ratio..it should be 0 ..huh..


Algebraic ways are given in posts above.

As for your other question. I think you misunderstood the problem.

There are 12 20-ounce and 36 40-ounce bottles. The average volume of those 48 bottles is 35 ounces.

We need to find how many of 36 40-ounce bottles must be sold for the average volume of the remaining bottles to be reduced to 25 ounces.
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink]

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shreygupta3192 wrote:
hi thanx for ur valuable answer but i`ll be glad if u could put it algebrically...that will be more easier for me to understand.

also, plz tell me wat is the point of "20 ounces bottles not sold" ... y r we still considering that while calculating the new ratio..it should be 0 ..huh..


Shrey,


We can establish from question

here x is number of 20 ounce bottles , y is 40 ounce bottles
x+y=48
20x+40y=1680

x=12,y=36
Coming to remaining part of question

Value of 20 ounce bottles will be 0 , if we consider the bottles sold.

20x+40z=25(x+z);

z = remaining bottles
x=12 , no removal here
20*12+40(z)=25(12+z);z=4

if remaining is 4 ,then 36-4 were sold=32.

However Brunel's approach is good time saving approach.
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink]

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New post 09 Mar 2015, 20:47
Bunuel wrote:
shreygupta3192 wrote:
A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?

(A) 10
(B) 20
(C) 30
(D) 32
(E) 34

hey can any1 plz tell me ..
if ques says that no 20 ounce bottles are sold..
then y r we considering "20*12" while calculating the new ratio..
wats the meaning and the use of that line above.." no 20 ounce bottles are sold"
y can`t we directly put 0 bottles for 20 ounces..

y can`t we go directly for ..

25=(20(0)+40(x))/x..

confused..:(


No. The question asks about the average weight of bottles which are not sold.

A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?

(A) 10
(B) 20
(C) 30
(D) 32
(E) 34

The current average of 20 (35 - 15) and 40-ounce (40 - 5) bottles is 35, thus there must be 3 times as many 40-ounce bottles as 20-ounce bottles. Since there are total of 48 bottles, then there must be 12 20-ounce bottles and 36 40-ounce bottles.

Now, we need to sell ONLY 40-ounce bottles so that the average to become 25. Same way, 25 is 5 away from 20 and 15 away from 40, so after selling some number of 40-ounce bottles, there must be 3 times as many 20-ounce bottles as 40-ounce bottles. So, there must be 12 20-ounce bottles and 12/3 = 4 40-ounce bottles.

Therefore, 36 - 4 = 32 40-ounce bottles must be sold.

Answer: D.

Hope it's clear.



Fantastic solution Bunuel, you are a legend !! :)
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink]

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New post 29 May 2015, 07:55
[48(35)-x(40) ] / (48-x) = 25

48(35) - x(40) = 48(25) - x(25)

48(10) = x(15)

48(2/3) = x

32= x
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink]

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Quote:
A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?
A.10
B.20
C.30
D.32
E.34


Let there be x 20 ounces bottles and y 40 ounces bottles.
Now, x + y = 48 (Given)

Given average volume of all 48 bottles is 35 ounces.
==> (20*x+ 40*y)/48 = 35
==> (20*x+ 40*y) = 35 * 48 -----(1)

Now let us assume k 40 ounces bottles are sold and then average volume of (48-k) bottles is 25.
==> (20*x+ 40*[y-k])/(48-k) = 25
==> (20*x+ 40*y - 40*k) = 25* (48 - k)
==> (35 * 48) - 40*k = 25*48 - 25*k
==> 15*k = 480
==> k = 32.

Hence D.
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink]

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dred wrote:
A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?
10
20
30
32
34


You can also resolve this question with weighted avg formula

20 40
\ /
35
/ \
15 5

Ratio : 3: 1 or we can say that 40 ounce bottles are three time as many as 20 ounce

so number of 40 ounce bottles are 36 and 20 ounce bottles are 12

next (20(12)+ 40x)/12+x = 25 -->where x is the remaining 40 ounce bottles

x= 4 i.e. 36-4=> 32 of 40 ounce bottles have been sold
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink]

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New post 07 Apr 2016, 11:55
email2vm wrote:
dred wrote:
A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?
10
20
30
32
34


You can also resolve this question with weighted avg formula

20 40
\ /
35
/ \
15 5

Ratio : 3: 1 or we can say that 40 ounce bottles are three time as many as 20 ounce

so number of 40 ounce bottles are 36 and 20 ounce bottles are 12

next (20(12)+ 40x)/12+x = 25 -->where x is the remaining 40 ounce bottles

x= 4 i.e. 36-4=> 32 of 40 ounce bottles have been sold



another solution:

Ratio is 3:1 ==>36 bottles of 40 ounces and 12 bottles of 20 ounces

again

40 20
\ /
25
/ \
5 15

1:3

36-x/12 =1/3

x=32
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New post 08 Apr 2016, 13:39
let t=#20 oz bottles
let f=#40 oz bottles
x=#40 oz bottles that have to be sold
equation 1: 20t+40f=(48)(35)=1680 oz
equation 2: 20t+40f-40x=25(48-x) oz
subtracting 2 from 1,
40x=480+25x
x=32 40 oz bottles have to be sold
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink]

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New post 22 Apr 2016, 18:08
its taking a bit longer to solve using the algebraic approach..
Anyone with any other approach?
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Re: A convenience store currently stocks 48 bottles of mineral water. The [#permalink]

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stonecold wrote:
its taking a bit longer to solve using the algebraic approach..
Anyone with any other approach?
Regards
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Hi,
the other method would be weighted average method.. people have already used it above, still ill do it once again..

TWO steps..


first - initial numbers
20 and 40 avail and average is 35..
so \(\frac{# of 20}{# of 40} = \frac{40-35}{35-20} = \frac{1}{3}\)
so # of 20 \(= \frac{1}{1+3} *48 =12\)..
and # of 40 ounces = 48-12 = 36

second -
20 and 40 avail and average is 25..
so\(\frac{# of 20}{# of 40} = \frac{40-25}{25-20} =\frac{3}{1}\)
so # of 20\(= \frac{3}{1+3} *x =12\), here we know # of 20 ounces remains constant..
so x= 16
and # of 40 ounces = 16-12 = 4..
now # of 40 ounces bottle sold = 36-4 = 32
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Re: A convenience store currently stocks 48 bottles of mineral water. The   [#permalink] 22 Apr 2016, 21:44
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