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A three digit number is such that twice the hundreds digits is thrice the hundred digit when they are reversed, it is increased by 594 find the number

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Let's call the three-digit number ABC, where A represents the hundreds digit, B represents the tens digit, and C represents the units digit
According to the given information:

  1. "Twice the hundreds digit is thrice the hundred digit when they are reversed" can be written as 2A = 3C.
  2. "It is increased by 594" means ABC + 594.
    Now, let's solve this system of equations:
    From 1: 2A = 3C
    From 2: ABC + 594
    We can use the fact that ABC is a three-digit number, so A cannot be 0. We'll start by trying values of A from 1 to 9.
    For A = 1:
    2(1) = 3C
    2 = 3C
    C = 2/3 (not an integer, so A = 1 doesn't work)
    For A = 2:
    2(2) = 3C
    4 = 3C
    C = 4/3 (not an integer)
    For A = 3:
    2(3) = 3C
    6 = 3C
    C = 6/3 = 2
    Now that we have found C = 2, we can find B:
    From the equation ABC + 594:
    32B + 594
    Since we know B is a digit, B can be any integer from 0 to 9.
    For B = 0:
    32(0) + 594 = 594 (not a three-digit number)
    For B = 1:
    32(1) + 594 = 626 (not a three-digit number)
    For B = 2:
    32(2) + 594 = 658 (a three-digit number)
    So, the three-digit number ABC is 658.

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