Question

a two digit number is such that the product of its digits is 35. when 18 is added to the number the digits interchange their places. find the number

Answer 1

x * y = 35
y * 10 + x + 18 = x * 10 + y

9 * y - 9 * x + 18 = 0

y = 35 / x

9 * 35 / x - 9 * x + 18 = 0

-9x² + 18x + 315 = 0

x = 7
y = 5