Quandaries and Queries


grade 6

First 8 is added to me, then I am multiplied by 6. Then 40 is subtracted from me. Finally, I am divided by 10. The result is 11. What number am I?


Hi Samantha,

The instructions are to start with a number and proceed as follows.

  1. add 8
  2. multiply by 6
  3. subtract 40
  4. divide by 10

The result is 11.

This is a "working backwards" problem. Let me get you started.

The final result was 11. It came from step 4 which says to divide by 10. Thus after step 3 you must have had 110 so that when you divided by 10 you got 11.

Now look at step 3. It says to subtract 40. You know the result was 110 so you must have had 150 so that subtracting 40 left 110. Thus, after step 2 you had 150.

Now look at step 2.

When you get back to the beginning go through the steps in order 1, 2, 3, and 4 to check that you get 11.