A number round off to 4000. The digit in the hundreds place is twice the digit in the tens place. The sum of the digits is 12. The numbers uses only two different digits. Find the number.
4*1000 + c*100 + b*10 + a*1
c < 5 so 0, 1, 2, 3 or 4
c = 2 b so c is even, 0, 2, or 4
4 + c + b + a = 12
so
c + b + a = 8
if c = 0 ,b = 0 because c=2b
4 0 0 4 does NOT add to 12.
if c = 2
4 2 1 mope, only two digits allowed
if c = 4
4 4 2 2
ah ha, 4422 seems to work
To find the number, we'll use a step-by-step approach based on the given conditions:
1. The number rounds off to 4000.
The number rounds off to 4000 means that it is closer to 4000 than to 3999. Therefore, the number must be greater than or equal to 3995 and less than 4005.
2. The digit in the hundreds place is twice the digit in the tens place.
Let's assume the digit in the tens place is 'x'. Since the digit in the hundreds place is twice the digit in the tens place, it would be '2x'.
3. The sum of the digits is 12.
The sum of the digits consists of the thousands, hundreds, tens, and units place digits. Therefore, we can write the equation as:
(4 + 2x + x + y) = 12, where 'y' would be the digit in the units place.
4. The number uses only two different digits.
Since we have assumed 'x' and 'y' as the digits, the number will use only these two digits.
Now, let's solve the equation and find the values of 'x' and 'y' to determine the number.
4 + 2x + x + y = 12
3x + y = 8 (Equation 1)
From the equation above, we can see that 'y' must be an even number, as 3x + y = 8.
Since we need to find the number closest to 4000, we can start by trying values for 'x' from 1 to 3, as 'x' cannot be higher since it is in the tens place.
Let's substitute the values of 'x' and solve the equation:
For x = 1:
3(1) + y = 8
3 + y = 8
y = 5
For x = 2:
3(2) + y = 8
6 + y = 8
y = 2
For x = 3:
3(3) + y = 8
9 + y = 8 (Not possible to get a valid value)
Therefore, the possible values for the number are:
1. 4150 (assuming x = 1 and y = 5)
2. 4260 (assuming x = 2 and y = 6)
Since the number rounds off to 4000, the closest number is 4150.
Hence, the number that satisfies all the given conditions is 4150.