A four digit number is between 3,000 and 4,000.The sum of its digits is 21.The product of the thousand and ones digits 24.The hundreds digit.What is the number?
So...
Your number is between 3000 and 4000
The sum of its digits is 21.
The product of the thousand and ones digits 24.
What about the hundreds digit?
Consider the number to be ABCD
We know that A = 3
so 3+B+C+D = 21
B+C+D = 17
"The product of the thousand and ones digits 24" ==== 3*D = 24
D = 8
That leaves B+C = 9
Once you have decided what the story is with the hundreds digit,
you will be able to finish it
so far we have:
3BC8 , where B+C = 9
To find the four-digit number, we need to analyze the given information step by step.
1. We know that the number is between 3,000 and 4,000. This means that the thousands digit must be 3, and the hundreds digit can only be from 0 to 9.
2. The sum of the digits is 21. Based on this information, we can find the sum of the thousands, hundreds, tens, and ones digits. Since the thousands digit is 3, we subtract that from 21, giving us 21 - 3 = 18 for the sum of the other three digits.
3. The product of the thousands and ones digits is 24. Since the thousands digit is 3, we divide 24 by 3, giving us 24 / 3 = 8 for the value of the ones digit.
4. Now, let's focus on the sum of the hundreds, tens, and ones digits. We know that these three digits should add up to 18, and the ones digit is 8. So, we subtract 8 from 18, which gives us 18 - 8 = 10 for the sum of the hundreds and tens digits.
5. We want to find the value of the hundreds digit, so let's assume that the tens digit is the largest possible number, which is 9. Then, the sum of the hundreds and tens digits would be 9 + 1 = 10. However, this doesn't work because we need the sum to be 10, not just the tens digit. Therefore, the tens digit must be smaller.
6. Let's try setting the tens digit to 8. In that case, the sum of the hundreds and tens digits would be 8 + 2 = 10, which is what we need. This means that the hundreds digit is 2.
7. Finally, we arrange the digits we have found: 3 (thousands digit), 2 (hundreds digit), 8 (tens digit), and 8 (ones digit). Therefore, the four-digit number that meets all the given conditions is 3288.