Question 709239
The Setup
Equation 1: {{{A + B = 9}}} (The sum of the digits is 9)
Equation 2: {{{10A + B + 45 = A + 10B}}} (The number is increased by 45 when the digits are reversed)
------------------------
Solution
Solve equation 1 for one of the variables. I will solve for A.
Equation 1: {{{A + B = 9}}}
{{{A = 9 - B}}}
Now plug (9-B) into equation 2 for A.
Equation 2: {{{10A + B + 45 = A + 10B}}}
{{{10(9-B) + B + 45 = (9-B) + 10B}}}
Multiply the 10 through.
{{{90 - 10B + B + 45 = 9 - B + 10B}}}
Combine like terms.
{{{135 - 9B = 9 + 9B}}}
Add 9B to both sides.
{{{135 = 9 + 18B}}}
Subtract 9 from both sides.
{{{126 = 18B}}}
Divide both sides by 18.
{{{highlight(7 = B)}}}
Now solve for A, while using 7 for B.
{{{A = 9 - B}}} {From earlier in the problem)
{{{A = 9 - (7)}}}
{{{highlight_green(A = 2)}}}
The number was 27.