A two digit number is such that the sum of the digit is ten.if the digits are reversed the new number fromed is less than the original number by 18.Find the number

1 answer

Let the tens digit be x and the units digit be y. We are given that x + y = 10 and that (10y + x) - (10x + y) = 18.

Expanding the second equation, we get 10y + x - 10x - y = 18. Simplifying further, we get 9y - 9x = 18, which can be simplified to y - x = 2.

Subtracting the equation y - x = 2 from x + y = 10, we obtain 2x = 8. Solving for x, we get x = 4.

Substituting x = 4 into the equation x + y = 10, we get 4 + y = 10. Solving for y, we get y = 6.

Therefore, the number is 46.