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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A certain organization sells boxes of 32 oranges for $8.00 per box
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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 boxBTGModeratorVI wrote: ↑Mon May 25, 2020 7:35 amA 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
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
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Solution:BTGModeratorVI wrote: ↑Mon May 25, 2020 7:35 amA 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
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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