Name three 4-digit numbers whose sum is 17,491
5830, 5830, 5831
To find three 4-digit numbers whose sum is 17,491, we can use a systematic approach to solve this problem.
Let's assume the three numbers are represented as ABCD, EFGH, and IJKL, where A, E, and I represent the thousands digit, B, F, and J represent the hundreds digit, C, G, and K represent the tens digit, and D, H, and L represent the ones digit.
We need to find three numbers whose sum is 17,491, so we can set up the following equation:
ABCD + EFGH + IJKL = 17,491
Now, let's break down the equation further. Since each number is 4-digit, the maximum value each digit can be is 9. This means that the minimum value each digit can be is 0. With this information in mind, we can proceed to solving the problem.
Starting from the right, we can focus on finding the ones place digit. Since the sum of all three digits in the ones place must equal 1 (from 17,491), there is only one possible combination: D + H + L = 1. Therefore, D, H, and L must be 0, 0, and 1 (in any order).
Moving to the tens place, the sum of the digits in the tens place must equal 9 (from 17,491). To achieve this, we can set up the following equation: C + G + K + 1 = 9. Since D and H are 0, we carried over a value of 1 to the tens place. Solving the equation, we find that C, G, and K must be 8, 0, and 0 (in any order).
Continuing to the hundreds place, we can set up a similar equation: B + F + J + 1 = 4. Because C, G, and K are all 0, we carry over a value of 1 to the hundreds place. Solving the equation, we find that B, F, and J must be 2, 1, and 0 (in any order).
Lastly, in the thousands place, we have A + E + I = 17 (from 17,491). Here, we have multiple possibilities. If we let A, E, and I be 9, 7, and 1 (in any order), the sum will equal 17.
Therefore, three 4-digit numbers whose sum is 17,491 can be represented as follows:
9B8D + 7F0H + 1J0L = 17,491
For example, one possible set of three numbers is:
9853 + 7060 + 1028 = 17,491