Boxes (help needed!!!) ?

Question

One hundred large boxes are placed on the table. Some of these boxes are selected and into each of them 8 smaller boxes are placed. Then some of these smaller boxes are selected and into each of them 8 smaller boxes are placed. This process is repeated a few times. At the end of this process there are 233 empty boxes altogether. How many boxes are there in total?

Answer 1

one way to model it is to put to only put 8 boxes into some of the large boxes and see if there is enough to make 233 boxes

so let x be number of boxes chosen with 8 smaller boxes inside

(100-x) + 8x = 233

100+ 7x = 233

7x =133

x = 19

so perferming this process only once allows 233 empty boxes

total boxes = 19+81 + 19* 8 = 252 boxes

hope this helps