Problem Solving

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

GMAT assassins aren't born, they're made,
Rich

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