a number rounds 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 number uses only two different digits.Find the number.
the number is between
3500 and 4500
So, now we start working with the info. The hundreds digit is even, so
363x
384x
400x
421x
442x
If the digits add to 12, that means we can have only
3630
4008
4215
4422
So, what do you think?
To find the number, let's break down the given information step by step:
1. The number rounds off to 4000: This means the number is closer to 4000 than any other number. Since it rounds off to 4000, we can conclude that the number is between 3950 and 4049.
2. The digit in the hundreds place is twice the digit in the tens place: Let's assume the tens digit is x. In that case, the hundreds digit would be 2x.
3. The sum of the digits is 12: We know that the hundreds digit (2x) and tens digit (x) should add up to 12. So we can set up the equation: 2x + x = 12.
Let's solve the equation:
2x + x = 12
3x = 12
x = 12 / 3
x = 4
Therefore, the tens digit is 4, and the hundreds digit is twice that, which is 8.
Now that we have the hundreds digit (8) and the tens digit (4), we can construct the number. The number will have 8 as the hundreds digit, 4 as the tens digit, and the units and thousands digit can be any of the two different digits mentioned in the problem.
So, the possible numbers are 8400 and 4800.
Thus, the number can be either 8400 or 4800.