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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?

Respuesta :

mhanifa

Answer:

  • 865

Step-by-step 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

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