Question

A two digit number is such that the product of the digit is 35 when 18 is added to the number the digits change their places . Find the number

Answer 1

Consider the number xy where:

xy = 10 . x + y

x . y = 35

xy + 18 = yx

10.x + y + 18 = 10.y + x

10.x - x = 10.y - y - 18

9.x = 9.y - 18

x = y - 2

(y - 2) . y = 35

y^2 - 2y - 35 = 0

Using the Bhaskara formula:

y = 7 (the negative solution is discarded)

x = 7 - 2

x = 5

Response: the xy number is 57.

;-)