. What number, whose sum of its digits is 26, becomes 6 000 when rounded to the nearest thousands?
check on the ones just below 6000
5BCD, where B+C+D = 21, and B ≥ 5
to round up to the nearest thousand you would simply look at the hundreds
if that is 5 or more you would round to 6000, they are:
5579 5588 5597 5669 5678 5687 5696 5759 5768 5777 5786 5795 5849 5858 5867 5876 5885 5894 5939 5948 5957 5966 5975 5984 5993
(note their digits add up to 26)
check on the ones just above 6000
6BCD, where B+C+D = 21, and B ≤ 4
there are less of these:
6299 6389 6398 6479 6488 6497
again, the sum of digits is 26 and they all round down to the nearest 6000
small correction, does not affect the numbers I found:
should say:
"check on the ones just above 6000
6BCD, where B+C+D = 20, and B ≤ 4"
(since the first digit starts with a 6, the remaining 3 add up to 20, not 21)
To find the number, we need to understand that its sum of digits is 26 and when rounded to the nearest thousands, it becomes 6,000.
Let's break down the problem into steps:
Step 1: Start by assuming the number is in the form of ABCD, where A, B, C, and D are digits (A represents the thousands, B represents the hundreds, C represents the tens, and D represents the units).
Step 2: According to the problem, the sum of its digits is 26. So, we can write an equation based on the assumption: A + B + C + D = 26.
Step 3: Now, let's consider rounding the number to the nearest thousands. This means the hundreds, tens, and units place should be zero. Therefore, our number becomes A000.
Step 4: According to the problem, when rounded to the nearest thousands, the number becomes 6,000. So, we can set up another equation: A000 = 6,000.
Step 5: Solving the equation A000 = 6,000, we find that A = 6.
Step 6: Now, substitute A = 6 into the equation A + B + C + D = 26. It becomes 6 + B + C + D = 26.
Step 7: Simplify the equation: B + C + D = 20.
Step 8: To find the possible values for B, C, and D, let's consider the constraints. Each digit can range from 0 to 9.
Step 9: Since B, C, and D can be any digits from 0 to 9, we need to find three digits that sum up to 20. After exploring the possible combinations, we can observe that B = 8, C = 6, and D = 6.
Step 10: Now, we have our number: 6,886. It satisfies both conditions - the sum of its digits is 26, and when rounded to the nearest thousands, it becomes 6,000.
Therefore, the number is 6,886.