By putting 8 boxes in a box, the total number of empty boxes increases by 8 - 1 = 7. If we call x the number of times that 8 boxes have been put in a box, we know that 11 + 7x = 102. It follows that x=13. In total, 11 + 13 × 8 = 115 boxes have been used.

It's a tough one.

Barbara uses 11 big boxed. that's for sure. Out of this, x big boxes are empty and 11-x boxes are filled - each with 8 medium boxes.

It comes to be that Barbara uses total of (11-x)*8 medium boxes. out of this y medium boxes are empty and (11-x)*8-y medium boxes contain small boxes - each contains 8 small boxes.

It comes to be that Barbara uses [(11-x)*8-y]*8 small boxes and it's GIVEN that all the small boxes are empty.

Now build the equation of the empty boxes:
x + y + [(11-x)*8-y]*8 = 102

Arranging the equation yields:
9x + y = 86

We know that x is between 1 and 10 (including) and y is between 1 and 79 (including) (it's given that there is at least one big and one medium empty boxes).

Now denote total amounts of big, medium and small boxes:

TB = 11
TM = (11-x)*8
TS = [(11-x)*8-y]*8

And try to put the numbers in the equation:

x=1 y=77 TS=24
x=2 y=68 TS=32
... ... ...

Finally calculate and add up the totals:

11 + 80 + 24 = 115
11 + 72 + 32 = 115
... ... ... = 115

As you can see, there might be various combinations of big, medium and small boxes that lead to the correct answer BUT there is only one correct answer.

Answer: 16 Boxes

Explanation
-----------
1. Barbara puts 8 standard boxes in 8 large boxes.
8 Large Boxes Are Used Here.

2. Barabara puts 8 small boxes in 8 standard boxes.
8 Standard Boxes Are Used Here.

3. Barabara Doesnt Keep Any Thing In Small Box.So, No Small Box Is Used.

Now Summarize The Used Boxes
i.e.
8 Large Boxes + 8 Standard Boxes

Total Boxes Used: 16

Abdul Raheem

The answer is 602

11 boxes of large one
8 boxes of standard one
8 boxes of small one

so, each of 11 large boxes may contain 8 boxes of standard one and each 8 standard boxes may contain 8 boxes of small one

so, 11 * 8 * 8 = 704 boxes total if there we will putting all the boxes none of one is empty..

now here specify that 102 boxes are empty so,

704 boxes - 102 empty boxes = 602 boxes which are used by Barbara is the total number of boxes..

i think she had a total of 118 Boxes
she puts 11 Large Boxes on the Table and out of the 11, she fill the 8 with standard Boxes giving 3 empty Boxe large and 8 empty Boxes standard, she then puts 8 small Boxes in the standard boxes that leaves 3 empty large and 8 small.
so if she has 102 empty boxes, then she has 16 full Boxes, added to the 102 gives u 118 boxes in total

soluion:
firstly, barbara put 11 standard boxes on the table,

let she filled 'n' large boxes each with '8' standard boxes,

so we have '11-n' empty large boxes
and '8n' empty standard boxes.

now let she filled 'm' standard boxes out of '8n' each with '8' small boxes,so we have '8n-m' empty standard boxes and '8m' empty small boxes.

so we have total '11-n' empty large boxes, '8n-m' empty standard boxes and 8m empty small boxes.

ATQ: (11-n)+(8n-m)+8m=102
=> n+m=13

so total boxes used: '11' large boxes, '8n' standard boxes and 8m small boxes

so: 11+8n+8m
11+8(n+m)
11+8*13 since n+m=13
115

115 total boxes used by barbara

himanshu

there are 11 large boxes.....

suppose (x) of them filled with std boxes each having 8.....

so 11-x large boxes are empty.

Each x large boxes are filled with 8 standard boxes each so total std boxes 8x of which y are empty(suppose).
and 8x-y are filled with small boxes each 8......

So now total empty boxes are 8(8x-y)small boxes + y std boxes + 11-x large boxes.
so simplifying this 11+63x-7y=102
solving by putting x=2 and y=5

so 11-2=9 large boxes are empty, y=5 std boxes are empty and 8(8x-y)=88 small boxes are empty

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