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A certain organization sells boxes of 32 oranges for $8.00 per box

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by BTGModeratorVI » Mon May 25, 2020 7:35 am

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A certain organization sells boxes of 32 oranges for $8.00 per box, boxes of 20 grapefruit for $7.00 per box, and combination boxes of oranges and grapefruit for $8.50 per box. If the unit price of each kind of fruit is independent of the kind of box in which it is packed and if each combination box contains twice as many oranges as grapefruit, how many grapefruit must be in a combination box?

A. 6
B. 7
C. 8
D. 10
E. 17

Answer: D
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Re: A certain organization sells boxes of 32 oranges for $8.00 per box

by Brent@GMATPrepNow » Thu May 28, 2020 9:17 am
BTGModeratorVI wrote: ↑
Mon May 25, 2020 7:35 am
 A certain organization sells boxes of 32 oranges for $8.00 per box, boxes of 20 grapefruit for $7.00 per box, and combination boxes of oranges and grapefruit for $8.50 per box. If the unit price of each kind of fruit is independent of the kind of box in which it is packed and if each combination box contains twice as many oranges as grapefruit, how many grapefruit must be in a combination box?

A. 6
B. 7
C. 8
D. 10
E. 17

Answer: D
Source: GMAT prep
A certain organization sells boxes of 32 oranges for $8.00 per box, boxes of 20 grapefruit for $7.00 per box
Price PER ORANGE = $8.00/32 = $1/4 = $0.25
Price PER GRAPEFRUIT = $7.00/20 = $0.35

Each combination box contains TWICE as many oranges as grapefruit
Let G = the NUMBER of grapefruit in the box
So, 2G = the NUMBER of oranges in the box

Combination boxes of oranges and grapefruit for $8.50 per box
We can write: (G)(0.35) + (2G)($0.25) = 8.50
Simplify: 0.35G + 0.5G = 8.50
Simplify: 0.85G = 8.50
Solve: G = 8.50/0.85 = 10

So, there are 10 grapefruit in the combination box

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: A certain organization sells boxes of 32 oranges for $8.00 per box

by Scott@TargetTestPrep » Thu May 28, 2020 3:31 pm
BTGModeratorVI wrote: ↑
Mon May 25, 2020 7:35 am
 A certain organization sells boxes of 32 oranges for $8.00 per box, boxes of 20 grapefruit for $7.00 per box, and combination boxes of oranges and grapefruit for $8.50 per box. If the unit price of each kind of fruit is independent of the kind of box in which it is packed and if each combination box contains twice as many oranges as grapefruit, how many grapefruit must be in a combination box?

A. 6
B. 7
C. 8
D. 10
E. 17

Answer: D
Solution:

We see that oranges cost 8/32 = $0.25 each and a grapefruit costs 7/20 = $0.35. If we let x = the number of grapefruit in a combination box, then 2x = the number of oranges in a combination box, and we can create the equation:

0.25(2x) + 0.35x = 8.5

0.5x + 0.35x = 8.5

0.85x = 8.5

x = 10

Answer: D

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