Question

I am a 3-digit number. If you switch my first and last digits, I decrease by 297. Also, my

middle digit is 6 less than my first digit, which is 2 less than 2 times my last digit. What
number am I?

Answer 1

• 865

Explanation:

Let the 3-digit number is abc = 100a + 10b + c.

We have:

• 100a + 10b + c - 100c - 10b - a = 297
• b = a - 6
• a = 2c - 2

Simplify the first equation:

• 99a - 99c = 297
• a - c = 3
• a = c + 3

Solve for c by substitution:

• 2c - 2 = c + 3
• 2c - c = 3 + 2
• c = 5

Find a:

• a = 3 + 5 = 8

Find b:

• b = 8 - 2 = 6

The number is:

• 865