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A fruit salad mixture consists of apples, peaches, and grapes. There

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A fruit salad mixture consists of apples, peaches, and grapes. There  [#permalink]

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New post Updated on: 15 May 2016, 06:20
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A fruit salad mixture consists of apples, peaches, and grapes. There are 3 times as many pounds of apples as grapes and 2.5 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 13 pounds per fruit, how many more pounds of apples than grapes does the mixture have?

(A) 15
(B) 12
(C) 9
(D) 6
(E) 5

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Originally posted by rxs0005 on 19 Dec 2010, 07:31.
Last edited by Bunuel on 15 May 2016, 06:20, edited 1 time in total.
Edited the question.
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Re: A fruit salad mixture consists of apples, peaches, and grapes. There  [#permalink]

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New post 19 Dec 2010, 07:43
rxs0005 wrote:
A fruit salad mixture consists of apples, peaches, and grapes. There are 3 times as many pounds of apples as grapes and times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 13 pounds per fruit, how many more pounds of apples than grapes does the mixture have?

(A) 15
(B) 12
(C) 9
(D) 6
(E) 5


Think there should be 2.5 times as many pounds of peaches as grapes.

Then if there are x pounds of grapes, then there are 3x pounds of apples and 2.5x pounds of peaches. As a mixture has an average of 13 pounds per fruit, (per 3 kind of fruits) then total weight of this mixture is 13*3=39.

So we have: x+2.5x+3x=39 --> x=6 --> apples-grapes=3x-x=12.

Answer: B.
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Re: A fruit salad mixture consists of apples, peaches, and grapes. There  [#permalink]

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New post 15 May 2016, 09:15
A+P+G= 13*3

A=3G
P=2.5G

3G+2.5G+G= 13*3
G= 13*3/6.5= 6

A= 6*3=18
Difference = 18-6=12
'B' is the answer
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Re: A fruit salad mixture consists of apples, peaches, and grapes. There a  [#permalink]

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New post 09 Jan 2018, 00:20
Bunuel wrote:
A fruit salad mixture consists of apples, peaches, and grapes. There are 3 times as many pounds of apples as grapes and 5/2 times as many pounds of peaches as grapes. If a mixture that has an average (arithmetic mean) of 13 pounds per fruit, how many more pounds of apples than grapes does the mixture have?

A. 15
B. 12
C. 9
D. 6
E. 5



If the mixture has an average of 13 pounds per fruit and there are 3 fruits,
the mixture contains a total of 39 pounds of fruit.

Let the total number of pounds of grapes be x.
The total number of pounds of apples is 3x.
Similarly, the total number of pounds of peaches is 5x/2

\(x+3x+\frac{5x}{2} = \frac{8x+5x}{2} = 39 => \frac{13x}{2} = 39 => x=6\)

We have been asked to find how many pounds extra of apples are
there in the mixture when compared to grapes, which is \(3x-x = 2x\) = 12(Option B)
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Re: A fruit salad mixture consists of apples, peaches, and grapes. There a  [#permalink]

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New post 11 Jan 2018, 07:07
Let the total weight of grapes, peaches and apples be g, p and a resp.
Let the total no. of fruits be t.
Then p=5/2 g and a=3g.
Total wt= g + 5/2g +3g = 13g/2
Since the avg wt is 13 pounds, we have (13g/2)/t = 13
which implies g/t=2, or g=2t

Ques asks for diff(wt of apples and grapes)= 3g-g=2g, i.e. 2(2t)=4t. (A multiple of 4).
(t is the total no. of fruits therefore t is a nat no.)
B is the only option that is a multiple of 4, hence B.
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Re: A fruit salad mixture consists of apples, peaches, and grapes. There a &nbs [#permalink] 11 Jan 2018, 07:07
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