PROBLEM 1-8-4

There were some toy cars on a shelf.  Sergio bought 1/3 of them.  Dalia bought 1/3 of what was left.  Reiko bought 1/3 of the remaining cars.  There are 8 cars left on the shelf. How many were there to start?

 

SOLUTION 1-8-4

Working backwards

If there are 8 cars left after Reiko bought 1/3 of them, which means that the 8 cars represents 2/3 of the cars before Reiko’s purchase.  Therefore, each third is 4 cars and then there were 12 cars before Reiko’s purchase. 

If there are 12 cars left after Dalia bought 1/3 of them, then the 12 cars represents 2/3 of the cars before Dalia’s purchase.  Therefore, each third is 6 and there were 18 cars before Dalia’s purchase.

If there were 18 cars left after Segio bought 1/3 of them, then the 18 cars represents 2/3 of the cars before Sergio’s purchase.  Therefore, each third is 9 and there were 27 cars before Sergio’s purchase.

It is possible to solve this algebraically, however, the equations get quite long!