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Average Price of fruit

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Average Price of fruit [#permalink] New post 26 May 2010, 06:26
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

100% (03:22) correct 0% (00:00) wrong based on 3 sessions
At a certain food stand, the price of each apple is $0.4 and the price of each orange is $0.6. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is $0.56. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is $0.52?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Kindly share your working & also mention the time in which you have solved the question.
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Re: Average Price of fruit [#permalink] New post 26 May 2010, 07:14
Hussain15 wrote:
At a certain food stand, the price of each apple is $0.4 and the price of each orange is $0.6. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is $0.56. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is $0.52?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Kindly share your working & also mention the time in which you have solved the question.


I got answer E

I know there is a fast way but I try to solve all these problems the same way
I use the letter "O" for oranges so it's not a zero after the .6

(.4A + .6O)/10 = .56 and A + O = 10
.4A + .6O = 5.6

Now subtract the above equation from A + O = 10
.4A + .6O = 5.6
-.4A - .4O = -4
.2O = 1.6
O = 8 so therefore A = 2

Now we try to find how many to take away to get the average of .52

.4(2) + .6(8-x) / 10-x = .52
.8 + 4.8 - .6x = 5.2 - .52x
5.6 - 5.2 = .6x - .52x
.04 = .08x
x = 5
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Re: Average Price of fruit [#permalink] New post 27 May 2010, 10:40
The initial average can be expressed as:

\frac{0.6x + 0.4(10-x)}{10} = 0.56, where x is the number of oranges.

4 + 0.2x = 5.6

x = 8

i.e. There were 2 apples and 8 oranges.

Now she puts back y oranges. The new average is:

\frac{0.6*(8-y) + 0.4*2}{10-y} = 0.52

5.6 - 0.6y = 5.2 - 0.52y

0.08y = 0.4

y = 5

So she puts back 5 oranges.
Pick E.

Takes about 1:15 to 1:30 to do this.
Re: Average Price of fruit   [#permalink] 27 May 2010, 10:40
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