This is my son's homework. could you please give me a good answer.?

Question

If you round me to the nearest thousand , you get 4,000.
The sum of my digits is 10.
If you read me forward or backward, I am the same.

What number am I?

Answer 1

ok, since this number is a palindrome we can represent it as abba, with a between 1 and 9 and b between 0 and 9. Since the sum of the digits is 2a+2b=10, a+b = 5. Since to the nearest thousand abba is 4000, a is either 3 or 4. If a is 4. then since a+b = 5, b must be 1. if a is 3, b must be 2. so this number is either 3223 or 4114.

However, 3223 rounded to nearest thousand is 3000, not 4000.

Thus it must be 4114.

Answer 2

1. Rounded to the nearest thousand is 4,000
2. Sum of digits = 10
3. Same forward and backward.

From clue 1, the number starts with either a 3 or a 4. It could be more than 3,500 or less than 4,500. Let's start with less than 4,500.

From clue 2, if the sum of the digits is 10, and you already know it's 4xxx, then the remaining 3 digits must add up to 6.

From clue 3, if it is the same backwards and forwards, and the first digit is 4 (4,000), then the last digit must be 4, so we're looking for 4xx4.

Now again from clue 2, the sum of the digits is 10. We already have 8 (4+4), so we need to make 2. Also, from 3, the two middle numbers must be the same (so it reads the same front and back). 1+1 is the only thing it could be, so the final number is 4114.


~~~~~~~~
Now trying 3xxx. The last number must be 3 -> 3xx3. From clue 2, 3+3 = 6, so the other 2 numbers must add up to 4. They must also be the same number. The only way to do that is with 2+2, which would give 3223. BUT, rounding 3223 to the nearest thousand would be 3,000.

Therefore, the only answer can be 4114.

Answer 3

So we know it is between 3500 and 4499 because that is the range that will round to 4,000
So we know that the first and last numbers are that same and either a 3 or 4, and we know that the two middle numbers are the same number, for reading forwards and backwards the same.

So possibilities are:
4444
4334
4224
4114
4004
3993
3883
3773
3663
3553

And
4 + 1 + 1 + 4 = 10

So 4114

Or algebraically:

4 + 4 + 2X = 10
8 + 2X = 10
2X = 2
X = 1
So: 4114

Checking 3
3 + 3 + 2X = 10
2X = 4
X = 2
So: 3223 Out of range!

Answer 4

The answer is 4114.

If you round me to the nearest thousand, you get 4000 means the number must be between 3500 and 4500

If you read me forward or backward, I am the same means the number must be 3XX3 or 4XX4.

If the sum of my digits is 10, then the number must be 3223 or 4114. However 3223 does not round to 4000 and violates the first condition. So the answer by a process of elimination is 4114

Answer 5

it so easy...just by the sentence you can get the answer..
a. nearest thousand 4,000
b. sum of digits 10
c. read forward or backward, the same

4+1+1+4=10.......so it's 4114

Answer 6

4114

since i new the first digit was 4, that would mean that the last digit would have to be 4. Now that only leaves that the sum of the digits is 10 while maintaining a mirror image, which would mean that the 2 middle digits would have to be the same, so

2x + 4 + 4 = 10
2x + 8 = 10
2x = 2
x = 1

so that gives me 4114

Answer 7

Wild guess 3223

Answer 8

Here is a website that will help you with any math problem.

Answer 9

4114

i cannot believe some of the answers im reading below here, this is elementary school math!!!

Answer 10

The answer is definetly 4,114.