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the 8 fruit boxes

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the 8 fruit boxes

by sanju09 » Thu May 13, 2010 6:02 am
A box of apples costs $2, a box of pears costs $3, and a box of plums costs $4. If 8 fruit boxes cost together cost $23, what is the largest possible number of the 8 fruit boxes that contain plums?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
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by Rahul@gurome » Thu May 13, 2010 6:30 am
Let there be x boxes of apples, y boxes of pears and z boxes of plums.
Then x + y + z = 8
2x + 3y + 4z = 23
Let us put the values of x , y and z in the above equation, 2x + 3y + 4z = 23,
such that z is maximum and x + y + z = 8.
If x = 4, y =1 and z = 3 then 2(4) + 3(1) + 4(3) = 23
So, the largest possible number of 8 fruit boxes that contain plums is 3.

The correct answer is (C).
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by kstv » Thu May 13, 2010 7:15 am
what Rahul@gurome has shown is the std. solution and in 2 mins not many smart solutions will come forth
still
total amount is $ 23
there has to be a box of pears = $ 3 , there cannot be even nos. of pear box
Left with $ 20
Answer options
E) 5 boxes of plums = $ 20 tot 6 boxes and no boxes of apples we need 8
D) 4 boxes of plums = $16 tot. 7 boxes getting close
C) 3 boxes of plums = $ 12 , 4 boxes of apples , tot 8

It is assumed that there should be atleast one box of each fruit.
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by clock60 » Thu May 13, 2010 12:30 pm
slightly detailed method of Rahul@gurome, let us go a little bit far
x+y+z=8
2x+3y+4z=23

multiply 1 st equation by 2 and substract

2x+2y+2z=16
2x+3y+4z=23

y+2z=7, and we need to max z, the largest value for z so y be an integer is 3, and y-1
1+2*3=7
so C
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