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The table above shows the average (arithmetic mean) price per dozen eg : Problem Solving (PS)
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Re: The table above shows the average (arithmetic mean) price per dozen eg [#permalink]
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As per the given info ratio of number of dozens sold in April:may:june as follows
April:may:june = 2/3:1:4/3

percentage distribution of three months, april= 2/9, may=1/3, june=4/9
now multiply price of each month with its percentage= (2/9*(1.26))+(1/3*(1.20))+(4/9*(1.08)= 1.16
hence answer is D
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Re: The table above shows the average (arithmetic mean) price per dozen eg [#permalink]
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Bunuel wrote:
abhishek1990p wrote:
Month Average Price
per Dozen
April $1.26
May $1.20
June $1.08

The table above shows the average (arithmetic mean) price per dozen of the large grade A eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?
(A) $1.08
(B) $1.10
(C) $1.14
(D) $1.16
(E) $1.18


Say x dozen eggs were sold in May.

Then 2x/3 dozen eggs were sold in April and 2*2x/3=4x/3 dozen eggs were sold in May.

Total x+2x/3+4x/3=3x dozen eggs were sold in three months.

Total sales: 2x/3*1.26+x*1.2+4x/3*1.08=$3.48x. The average price per dozen 3.48x/3x=$1.16.

Answer: D.


Hi,

This type of calculation takes more than 3 mins.

Is there any easy way of solution?

Regards,
Rrsnathan.
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Re: The table above shows the average (arithmetic mean) price per dozen eg [#permalink]
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Bunuel wrote:
Month Average Price
per Dozen
April $1.26
May $1.20
June $1.08

The table above shows the average (arithmetic mean) price per dozen of the large grade A eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?
(A) $1.08
(B) $1.10
(C) $1.14
(D) $1.16
(E) $1.18


Say x dozen eggs were sold in May.

Then 2x/3 dozen eggs were sold in April and 2*2x/3=4x/3 dozen eggs were sold in May.

Total x+2x/3+4x/3=3x dozen eggs were sold in three months.

Total sales: 2x/3*1.26+x*1.2+4x/3*1.08=$3.48x. The average price per dozen 3.48x/3x=$1.16.

Answer: D.[/quote]


Hi Bunuel,

could you tell me where am i going wrong?
if suppose x dozen eggs were sold in april then
1.26X+1.20(3/2X)+1.08(2X)/X+3/2X+2X

but i am not getting the answer
please tell me where am i going wrong?
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Re: The table above shows the average (arithmetic mean) price per dozen eg [#permalink]
Expert Reply
saggii27 wrote:
Bunuel wrote:
Month Average Price
per Dozen
April $1.26
May $1.20
June $1.08

The table above shows the average (arithmetic mean) price per dozen of the large grade A eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?
(A) $1.08
(B) $1.10
(C) $1.14
(D) $1.16
(E) $1.18


Say x dozen eggs were sold in May.

Then 2x/3 dozen eggs were sold in April and 2*2x/3=4x/3 dozen eggs were sold in May.

Total x+2x/3+4x/3=3x dozen eggs were sold in three months.

Total sales: 2x/3*1.26+x*1.2+4x/3*1.08=$3.48x. The average price per dozen 3.48x/3x=$1.16.

Answer: D.



Hi Bunuel,

could you tell me where am i going wrong?
if suppose x dozen eggs were sold in april then
1.26X+1.20(3/2X)+1.08(2X)/X+3/2X+2X

but i am not getting the answer
please tell me where am i going wrong?[/quote]

(1.26x+1.20(3/2*x)+1.08(2x))/(x+3/2*x+2x) is correct. Check math.
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Re: The table above shows the average (arithmetic mean) price per dozen eg [#permalink]
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abhishek1990p wrote:
Month Average Price
per Dozen
April $1.26
May $1.20
June $1.08

The table above shows the average (arithmetic mean) price per dozen of the large grade A eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?
(A) $1.08
(B) $1.10
(C) $1.14
(D) $1.16
(E) $1.18



You can approximate here.

April - 1.26
May - 1.20
June - 1.08

"If 2/3 as many dozen were sold in April as in May" - The price difference between April and May is 0.06. Splitting this in 2:3 ratio such that average is closer to May, the avg price of April-May would be about 1.22.

"twice as many were sold in June as in April" - In June, number of dozens sold were twice the number in April. So average of April-May-June would be closer to average of April-May but about in the centre.
Mid point of 1.22 and 1.08 is 1.15 but it should be closer to 1.22 so the average must be 1.16.

Answer (D)
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Re: The table above shows the average (arithmetic mean) price per dozen eg [#permalink]
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Hi All,

We're told that the table above shows the average (arithmetic mean) price per dozen eggs sold in a certain store during three successive months - and that 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April. We're asked for the average price per dozen of the eggs sold over the three-month period. This question can be solved by TESTing VALUES and doing the necessary Arithmetic. It's also worth noting that since the answers are relatively 'close' together, we will have to be precise with our calculations.

IF....
2 dozen eggs were sold in April
3 dozen eggs were sold in May
4 dozen eggs were sold in June

Total price = (2)($1.26) + (3)($1.20) + (4)($1.08) = $2.52 + $3.60 + $4.32 = $10.44
Average price per dozen = $10.44/9 = $1.16

Final Answer:

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Re: The table above shows the average (arithmetic mean) price per dozen eg [#permalink]
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abhishek1990p wrote:

The table above shows the average (arithmetic mean) price per dozen eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?

A. $1.08
B. $1.10
C. $1.14
D. $1.16
E. $1.18

PS40502.01

Attachment:
2019-09-21_1453.png



We can create the equations:

A = 2M/3

3A = 2M

3A/2 = M

1.5A = M

and

J = 2A

Therefore, the average price per dozen eggs sold over the three-month period is:

(A x 1.26 + 1.5A x 1.20 + 2A x 1.08)/(A + 1.5A + 2A)

(1.26A+ 1.8A + 2.16A)/(4.5A)

5.22A/(4.5A) = 5.22/4.5 = 1.16

Alternate solution:

We can let the number of dozens of eggs sold in May be 6; thus, the number of dozens of eggs sold in April is 2/3 x 6 = 4, and the number of dozens of eggs sold in June is 2 x 4 = 8.

Therefore, the average price per dozen eggs sold over the three-month period is:

(4 x 1.26 + 6 x 1.20 + 8 x 1.08) / (4 + 6 + 8)

20.88/18 = 1.16

Answer: D
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Re: The table above shows the average (arithmetic mean) price per dozen eg [#permalink]
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Bunuel wrote:
abhishek1990p wrote:
Month Average Price
per Dozen
April $1.26
May $1.20
June $1.08

The table above shows the average (arithmetic mean) price per dozen of the large grade A eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?
(A) $1.08
(B) $1.10
(C) $1.14
(D) $1.16
(E) $1.18



Say x dozen eggs were sold in May.

Then 2x/3 dozen eggs were sold in April and 2*2x/3=4x/3 dozen eggs were sold in May.

Total x+2x/3+4x/3=3x dozen eggs were sold in three months.

Total sales: 2x/3*1.26+x*1.2+4x/3*1.08=$3.48x. The average price per dozen 3.48x/3x=$1.16.

Answer: D.

Hey Bunuel you've got a typing mistake... It's in june where 4x/3 eggs were sold.... not in May.
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patto wrote:
Bunuel wrote:
abhishek1990p wrote:
Month Average Price
per Dozen
April $1.26
May $1.20
June $1.08

The table above shows the average (arithmetic mean) price per dozen of the large grade A eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?
(A) $1.08
(B) $1.10
(C) $1.14
(D) $1.16
(E) $1.18



Say x dozen eggs were sold in May.

Then 2x/3 dozen eggs were sold in April and 2*2x/3=4x/3 dozen eggs were sold in May.

Total x+2x/3+4x/3=3x dozen eggs were sold in three months.

Total sales: 2x/3*1.26+x*1.2+4x/3*1.08=$3.48x. The average price per dozen 3.48x/3x=$1.16.

Answer: D.

Hey Bunuel you've got a typing mistake... It's in june where 4x/3 eggs were sold.... not in May.

___________________
Edited. Thank you.
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Re: The table above shows the average (arithmetic mean) price per dozen eg [#permalink]
Ans - D

Total x+2x/3+4x/3=3x dozen eggs were sold in three months.

Total sales: 2x/3*1.26+x*1.2+4x/3*1.08=$3.48x. The average price per dozen 3.48x/3x=$1.16.

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Re: The table above shows the average (arithmetic mean) price per dozen eg [#permalink]
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We can apply a weighted average concept twice here.

Better to start with June and April since they have a nice ratio of 2:1.
The difference in prices 1.26-1.08=0.18 so June=April=1.08+0.18/3=1.14

And once again
JuneApril:May=2:1 The difference in prices 1.20-1.14=0.06 so three-month average = 1.14+0.06/3=1.16
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Re: The table above shows the average (arithmetic mean) price per dozen eg [#permalink]
Two approaches:

April : May: June
2: 3: 4

2(1.26) + 3(1.20) + 4(1.08) = 2.52 + 3.60 + 4.32 = 10.44

10.44 / 9 = $1.16

Weighted average approach:

April : June = 1 : 2

1.26 - 1.08 = .18
.18 / 3 = .06

The weighted average between April and May is $1.14

April & June : May = 2:1

1.20 - 1.14 = 0.06 / 3 = 0.02

1.14 + 0.02 = 1.16

Answer is D.
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Re: The table above shows the average (arithmetic mean) price per dozen eg [#permalink]
abhishek1990p wrote:

The table above shows the average (arithmetic mean) price per dozen eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?

A. $1.08
B. $1.10
C. $1.14
D. $1.16
E. $1.18

Attachment:
2019-09-21_1453.png

1. Let's say a total of \(90\) eggs were sold during the 3 month period
Quote:
If 2/3 as many dozen were sold in April as in May

2. Let the eggs sold in May be \(x\), then the eggs sold in April were be \(\frac{2}{3}x\)
Quote:
twice as many were sold in June as in April

3. We know that the eggs sold in April were \(\frac{2}{3}x\), hence the eggs sold in June were \(\frac{4}{3}x\)

4. Now, \(x + \frac{2}{3}x + \frac{4}{3}x = 90 \) -> \(\frac{3}{3}x + \frac{2}{3}x + \frac{4}{3}x = 90\) -> \(9/3x = 90 \) -> \(x = 30\)

5. Substituting \(x = 30\) we get that the eggs sold in May were \(30\), April were \(20\) and June were \(40\)

6. The average price for the 3 months is:

\(\frac{Eggs sold in April * Average price in April + Eggs sold in May * Average price in May + Eggs sold in May * Average price in June}{Eggs sold in April + Eggs sold in May + Eggs sold in June}\)

\(\frac{20 * 1.20 + 30 * 1.26 + 40 * 1.08}{20 + 30 + 40}\) \(=\) \(\frac{37.8 + 24 + 43.2}{90}\) \(=\) \(\frac{105}{90}\) \(=\) \(1.16\)

Ans. D
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Re: The table above shows the average (arithmetic mean) price per dozen eg [#permalink]
KarishmaB wrote:
Quote:
11 Rules for Postingabhishek1990pMonth Average Price
per Dozen
April $1.26
May $1.20
June $1.08

The table above shows the average (arithmetic mean) price per dozen of the large grade A eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?
(A) $1.08
(B) $1.10
(C) $1.14
(D) $1.16
(E) $1.18


You can approximate here.

April - 1.26
May - 1.20
June - 1.08

"If 2/3 as many dozen were sold in April as in May" - The price difference between April and May is 0.06. Splitting this in 2:3 ratio such that average is closer to May, the avg price of April-May would be about 1.22.

"twice as many were sold in June as in April" - In June, number of dozens sold were twice the number in April. So average of April-May-June would be closer to average of April-May but about in the centre.
Mid point of 1.22 and 1.08 is 1.15 but it should be closer to 1.22 so the average must be 1.16.

Answer (D)

­Would it be possible to elaborate please?

Thank you
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