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
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.
198
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).
To find your special number, let's break down the information given step by step:
1. Your special number has a 9 in the units column.
2. If you remove the 9 from the units column and place it at the left-hand end of the number, you get a new number.
3. This new number is four times your special number.
Let's call your special number "x." Based on the information given, we can create the following equation:
4x = 10x + 9
Here's how we derived the equation:
1. As your special number has a 9 in the units column, we represent it as 10x + 9, where x is the unknown digit(s) that appear before the 9.
2. When we move the 9 to the left-hand end, the new number becomes 9 * 10^(number of digits in x) + x. The number of digits in x can be found by calculating the logarithm of x (base 10) and rounding up to the nearest whole number.
3. As the new number is four times your special number, we multiply 10^(number of digits in x) by 4 and add x.
Now, let's solve the equation to find the value of x:
4x = 10x + 9
Simplifying the equation:
4x - 10x = 9
-6x = 9
Dividing both sides by -6:
x = 9/-6
x = -3/2
Therefore, your special number is -3/2.