Question : Barbara has boxes in three sizes: large, standard, and small. She puts 11 large boxes on a table. She leaves some of these boxes empty, and in all the other boxes she puts 8 standard boxes. She leaves some of these standard boxes empty, and in all the other standard boxes she puts 8 (empty) small boxes. Now, 102 of all the boxes on the table are empty. How many boxes has Barbara used in total?

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:

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.

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

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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