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Re: A certain organization sells boxes of 32 oranges for $8.00 per box, bo [#permalink]
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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


Bunuel wrote:
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


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Re: A certain organization sells boxes of 32 oranges for $8.00 per box, bo [#permalink]
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
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Re: A certain organization sells boxes of 32 oranges for $8.00 per box, bo [#permalink]
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
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Re: A certain organization sells boxes of 32 oranges for $8.00 per box, bo [#permalink]
Expert Reply

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
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Re: A certain organization sells boxes of 32 oranges for $8.00 per box, bo [#permalink]
Expert Reply
Bunuel wrote:
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



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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Re: A certain organization sells boxes of 32 oranges for $8.00 per box, bo [#permalink]
\(\frac{8}{32} = 0.25\) 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.
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Re: A certain organization sells boxes of 32 oranges for $8.00 per box, bo [#permalink]
Expert Reply
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

=> \(\frac{[28G + 40G] }{ 80}\) = 8.50

=> 68G = 8.50 * 80 = 680

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

Answer D
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Re: A certain organization sells boxes of 32 oranges for $8.00 per box, bo [#permalink]
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Re: A certain organization sells boxes of 32 oranges for $8.00 per box, bo [#permalink]
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