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.