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A fruit salad mixture consists of apples, peaches, and grape

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A fruit salad mixture consists of apples, peaches, and grape

by BTGmoderatorAT » Thu Jan 11, 2018 6:26 am
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

Is there a strategic approach to this question? Can any experts assist?
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by EconomistGMATTutor » Thu Jan 11, 2018 8:46 am
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

Is there a strategic approach to this question? Can any experts assist?
The fruit salad mixture consists of three fruits; apples, peaches and grapes.
The mixture has an average of 13 pounds per fruit, therefore, total weight of the salad will be:
$$=13\times3=39\ pounds$$

Let the grapes be x pounds, then,
apples = 3x
peaches = 5x/2

$$x+3x+\frac{5}{2}x=39$$
$$4x+\frac{5}{2}x=39$$
$$\frac{8x+5x}{2}=39$$
$$\frac{13x}{2}=39$$
$$x=39\times\frac{2}{13}$$
$$x=3\times2=6$$

Therefore, grapes are 6 pounds.

We are asked to find how many more pounds of apples than grapes does the mixture have?
$$Apples\ =\ 3x=3\times6=18pounds$$

Therefore, apples are 18 - 6 = 12 pounds more than grapes in the mixture.

Hence, Option B is correct.

Hope it helps.
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by [email protected] » Thu Jan 11, 2018 11:08 am
Hi ardz24,

We're told that 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. We're told that a mixture has an AVERAGE of 13 pounds of EACH of the 3 fruits. We're asked how many MORE pounds of apples than grapes the mixture has.

Since the total amount of fruit in the mixture is relatively small, we can do a bit of 'brute force' arithmetic to answer this question. To start, with an AVERAGE of 13 pounds of each type of fruit, there would be 3(13) = 39 total pounds of fruit in the mixture. Given the ratios of fruit involved, we know...

IF.....
we have 1 pound of grapes, then we have 3 pounds of apples and 2.5 pounds of peaches.... total weight = 1+3+2.5 = 6.5 pounds
with 2 pounds of grapes, we have 6 pounds of apples and 5 pounds of peaches... total weight = 2+6+5 = 13 pounds
Etc.

Notice that if we TRIPLE the second option, then we'll have 39 total pounds of fruit...
6 pounds of grapes, 18 pounds of apples and 15 pounds of peaches... total weight = 6+18+15 = 39 pounds.

The 39-pound total is an exact match for what we were told, so we know there are 18 pounds of apples and 6 pounds of grapes. Thus, there are 18-6 = 12 MORE pounds of apples than grapes in the mixture.

Final Answer: B

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by Scott@TargetTestPrep » Thu Jan 18, 2018 7:55 am
ardz24 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
We can let the number of pounds of apples = a, the number of pounds of peaches = p, and the number of pounds of grapes = g and create the equations:

a = 3g

and

p = 5g/2

We also know that the total number of pounds in the mixture is 3 x 13 = 39, thus:

a + p + g = 39

Substituting to get all our variables in terms of g, we have:

3g + 5g/2 + g = 39

Multiplying by 2 we have:

6g + 5g + 2g = 78

13g = 78

g = 6

So a = 18. There are 12 more pounds of apples than there are of grapes.

Answer: B

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by DrMaths » Thu Jan 18, 2018 8:56 am
Write a triple ratio
Apples:Peaches:Grapes
3:5/2:1
Double it to get whole numbers
6:5:2 which has a total of 6 + 5 + 2 = 13 parts (which matches the question nicely, PER FRUIT)
As there are 3 fruits, multiply by 3
18:15:6 = 39 parts
Subtract Apples - Grapes = 18 - 6 = 12
Job done.
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