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

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.

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