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

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Math Expert
Joined: 02 Sep 2009
Posts: 43792
A fruit salad mixture consists of apples, peaches, and grapes. There a [#permalink]

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08 Jan 2018, 23:00
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93% (03:27) correct 7% (00:00) wrong based on 15 sessions

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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 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
[Reveal] Spoiler: OA

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

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08 Jan 2018, 23:20
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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Joined: 16 May 2017
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Re: A fruit salad mixture consists of apples, peaches, and grapes. There a [#permalink]

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11 Jan 2018, 06:07
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.
Re: A fruit salad mixture consists of apples, peaches, and grapes. There a   [#permalink] 11 Jan 2018, 06:07
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