The Method of “False Position”

Problem: Kristina has a quantity of toys. The quantity and its 1/8 added together equals the total number of Mia's toys, which is 18. How many toys does Kristina have?

Assume the quantity is 8:

1                                      8

1/8                   1

Total                9

As many times as 9 must be multiplied to get 18, so many times 8 must be multiplied to give the required number. Multiply 9 to get 18:

1                                      9

2                                    18

                                    Total    2

Multiply 2 by 8 to get

1                                       2

2                                       4

4.                        8           

8                     16

The quantity is                                             16

                                                1/8                   2

                                                Total               18

Therefore, Kristina has 16 toys in total.