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

Question

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

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

PS20477

BrentGMATPrepNow · Accepted Answer

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

Siak0730 · Answer

"If the unit price of each kind of fruit is independent of the  kind  of box in which it is packed" ---- this is to create unwanted confusion.
Given:
I. boxes of 32 oranges for $8.00 per box
price per orange="a"= 8$/32= (1/4)$ ----- (i)

II. boxes of 20 grapefruit for $7.00 per box
price per grapefruit="b"= 7$/20 ----- (ii)

III. combination boxes of oranges and grapefruit for $8.50 per box
let x be the number of oranges and y be the number of grapefruits in combination box
==> 8.5$=(x*a+y*b) ------ (iii)

IV. each combination box contains twice as many oranges as grapefruit
x=2y ----- (iv)

substituting (i), (ii), and (iv) in (iii) we get (or values of a, b and value of x in terms of y)
8.5$= (1/4)$*2y + (7/20)$*y 
or
8.5= (5/20)*2y + (7/20)$*y
or
8.5= (17/20)*y
or y=10
or
number of grapefruits in combination box = 10 = option D

Archit3110 · Answer

rate per orange ; 8/32 ; 1/4 and rate per gf = 7/20 
so for a box of both price ; 8.5 $
which contains ; 1/4 * oranges + 7/20 * gf
and given o=2*gf
so 
8.5 = 1/4*2*gf + 7/20 * gf
solve for gf = 10
OPTION D

NitishJain · Answer

D

32 oranges price --- $8
1 orange price ------1/4

20 grapefruit price---- $7
1 grapefruit price---------7/20

Combination Box:
orange = 2 graprefruit
o =2g;

Also; No of oranges * price of one orange + No of grapefruit * price for one grapefruit = $8.5

o*(1/4) + g*(7/20) = 85/10
2g(1/4) + g*(7/20) = 85/10

2g(5/20) + g*(7/20) = 85/10
17g/20 = 85/10
g= 10

anniaustin · Answer

1 orange costs = $8/32 = $0.25
1 grapefruit costs = $7/20 = $0.35
Let number of grapefruit in a combination box = g
Therefore, (0.25*2g) + (0.35*g) = 8.50
Solving for g, 
g=10

Answer:  D

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given that
 • A certain organization sells 
 o boxes of 32 oranges for $8.00 per box
o boxes of 20 grapefruit for $7.00 per box
o combination boxes of oranges and grapefruit for $8.50 per box

• Each combination box contains twice as many oranges as grapefruit

To find  
We need to determine
 • The number of grapefruits in a combination box

Approach and Working out  
 • Cost of 1 orange = 8/32 = $0.25
• Cost of 1 grapefruit = $7/20
• Thus, $8.5 = 0.25(2x) + 7x/20 (where x represents the number of grapefruits in a combination box)
 o Implies, x = 10

Therefore, Option D is the correct answer.

Correct Answer: Option D

ScottTargetTestPrep · Answer

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

Basshead · Answer

\frac{8}{32} = 0.25  per orange
 \frac{7}{20} = 0.35  per grapefruit

A combination box = $8.50

0.25(2x) + 0.35(x) = 8.50

0.5x + 0.35x = 8.50

0.85x = 8.50

x = 10

Answer is D.

MathRevolution · Answer

Oranges: O
Grapefruit: G

Combination box: G + O = $8.50

=> G *  \frac{7}{20}  + O *  \frac{8}{32}  = 8.50

=> Since, O = 2G

=> G *  \frac{7}{20}  + 2G *  \frac{8}{32}  = 8.50

=>  \frac{(7G)}{(20)}  +  \frac{(8G)}{(16)}  = 8.50

=>  \frac{  }{ 80}  = 8.50

=> 68G = 8.50 * 80 = 680

=> G =  \frac{680}{68}  = 10

Answer D

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

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