Question 475317
Let the 2-digit number be AB, where A is in the ten's place and B is in the one's place.
The value of AB is 10*A + B
If you reverse the order to BA then the value is 10*B + A
Set up equations:
We know the sum of A and B is 12. We know the value of BA is 18 more than value of AB.
{{{A + B = 12}}}
{{{10B + A = 10A + B + 18}}}
Combine like terms in 2nd equation
Subtract B on both sides, Subtract A on both sides
{{{9B = 9A + 18}}}
Divide by 9 on both sides
{{{B = A + 2}}}
Now substitute A+2 for B in 1st equation:
{{{A + (A+2) = 12}}}
{{{2A + 2 = 12}}}
Subtract 2 on both sides
{{{2A = 10}}}
Divide by 2 on both sides
{{{A = 5}}}
B = A + 2 = 5+2 = 7
Therefore the original number (AB) is 57