Question

My special number has an 9 in the units column .If I remove the 9 from the units column and place it at the left hand end of the number ,but leave all the other digits unchanged,I get a new number .This new number is four times my special number.What is my special number

Answer 1

198

Answer 2

Let's call the original number "ab9", where a and b represent the tens and hundreds digits (respectively).

When we move the 9 to the left and shift the other digits over, the new number becomes "9ab" (which is equivalent to 900 + 10a + b).

We know that this new number is four times the original, so we can set up an equation:

4(ab9) = 9ab

Expanding both sides:

4(100a + 10b + 9) = 900 + 10a + b

Simplifying:

400a + 40b + 36 = 900 + 10a + b

Collecting like terms:

390a + 39b = 864

Dividing by 39:

10a + b = 22

So our special number is ab9, where a and b add up to 2 and a is less than or equal to 1 (since otherwise we would have a two-digit number for "ab").

The only solution that fits these constraints is 198, since 1 + 9 + 8 = 18 and 1 is the only possible value for a.

Therefore, the special number is 198, and when we move the 9 to the left we get 9198, which is four times the original.

Answer 3

Correct! The special number is 198. When we move the 9 to the left, we get 9198, which is four times the original number (198).