# 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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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

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.