Find a three digit number, knowing that the sum of the first two digits is 12 , the difference of the last two is 3 and the sum of all three digits is 15

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Find a three digit number, knowing that the sum of the first two digits is 12, the difference of the last two is 3 and the sum of all three digits is 18.

We note: with a - the first digit, b - the second digit, c - the third digit

Because

a + b + c = 18

a + b = 12

We will calculate the third digit which is equal to the difference of the two sums

c = 18 - 12

c = 6

Knowing the last digit and that the difference of the first two digits is 3 , the second digit is going to be

b = c + 3

b = 9

We calculate the last digit by subtracting from the given sum the two known digits

18 - c - b

18 - 6 - 9 = 3

a = 3

We will write the number

abc

396

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