The sum of the digits of a certain two-digit number is 6. Reversing its digits decreases the number by 54. Find the number.

Answer 1

You have 2 unknowns. Therefore, you need to create 2 equations.

Call the digits A & B.

The value is 10A + B

From the 1st sentence we have A + B = 6

From the second sentence, we can write:

10A + B - 54 = 10B + A ((the value - 54 = the value after reversing the digits))

Simplify:

9A - 9B = 54

multiply the 1st equation by 9 to get:

9A + 9B = 54

add the equations to get:

18A = 108

So A = 6, and B = 0

CHECK: A + B = 6

60 - 54 = 6

Answer 2

Let N be the 2-digit number

x be the 10s digit

y by the 1s digit

Then x + y = 6, and

10x + y = N, and

10y + x = N - 54

Then we just have 3 linear equations in 3 unknowns, and we can use substitution or your favorite method to solve. I solved for N first, since that is what we are trying to find, and got N = 60.