Write down a 3-digit number where digits are in decreasing order. Reverse the digits and subtract it from the first number.
1 answer:
Step-by-step explanation:
987 → 789
987 - 789 = 198
876 → 678
876 - 678 = 198
765 → 567
765 - 567 = 198
654 → 456
654 - 456 = 198
543 → 345
543 - 345 = 198
432 → 234
432 - 234 = 198
321 → 123
321 - 123 = 198
Generally it is always like that:
3 ≤ x ≤ 9
100x + 10(x-1) + (x - 2) → 100(x - 2) + 10(x - 1) + x
(100x + 10(x - 1) + (x - 2)) - (100(x-2) + 10(x-1) + x)
= 100x + 10(x - 1) + (x - 2) - 100(x - 2) - 10(x - 1) - x <em>cancel 10(x - 1)</em>
= 100x + x - 2 - 100x + 200 - x <em>cancel 100x and x</em>
= 100 - 2
= 198
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