two digit number

Question

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The sum of the digits of a certain two digit nuber is 12. when you reverse its digits you increase the number by 18.find the number

Guest Mar 1, 2021

CubeyThePenguin · Answer 1 · 2021-03-01T02:38:36

two digit number AB ==> 10A + B

A + B = 12 . (1)

(10A + B) - (10B + A) = 18 ---> 11A - 9B = 18 . (2)

Solve the system.

A = 7

B = 5

The number is 75.

CPhill · Answer 2 · 2021-03-01T09:30:16

Call the number 10a + b

a + b = 12 ⇒ b = 12 - a (1)

10b + a = 10a + b + 18 (2)

Sub (1) into (2)

10(12 - a) + a = 10a + 12 - a + 18

120 - 9a = 9a + 30

120 - 30 = 18a

90 = 18a

a = 90 / 18 = 5

b = 7

The number is 57

57 + 18 = 75 !!!