When you reverse the digits in a certain two digit number you decrease its value by 54. Find the number if the sum of its digits is 6.

Question

Could you be specific because I don't understand these types of questions.

Answer 1

Use X and Y for the digits, with X being the "tens" digit.

The value of the number is then 10X + Y

We're also told that reversing the digits decreases the value by 54.

Thus:

10Y + X = 10X + Y - 54

simplify and rearrange into a standard format:

-9X + 9Y = -54 (equation 1)

We are also told that X + Y = 6, therefore X = 6 - Y. Use this expression to replace X in equations 1:

-9(6 - Y) + 9Y = -54

Simplify and solve to get Y = 0

Therefor, the number is 60. To prove it, reverse the digits to get 6, and the value is reduced by 54.