Problema Solution
A three digit number consists of 7, 8 and one more number. When these digits are reversed and subtracted from the original number the answer yielded will be consisting of the same digits arranged yet in a different order. Solve the word problem and find the another digit?
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Solution:
Let the unknown digit = n.
The given number is then,
700 + 80 + n = 780 + n.
When reversed the new number is,
100n + 80 + 7 = 87 + 100n.
Subtracting these two numbers we get,
After solving, we get
693 = 99n.
The digit can be arranged in 3 ways or 6 ways.
We have already investigated 2 of these ways.
We can now try one of the remaining 4 ways. One of these are n = 95
100n + 70 + 8 = 693 - 99n
199n = 615
After solving, we get
n = 3
Answer:
The unknown digit is 3.