Question 700041
The set up is tricky for this problem.
Let A equal one of the numbers
Let B equal one of the numbers
A & B are one digit numbers so they are positive but less than 10
Equation 1: {{{A + B = 8}}}
Equation 2:{{{10A + B + 18 = A + 10B)}}}
The numbers are multiplied by 10 to put them in the tens place.
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Solve equation 1 for one of the variables
Equation 1: {{{A + B = 8}}}
{{{A = 8 - B}}}
Now plug (8 - B) into equation 2 for A
Equation 2:{{{10A + B + 18 = A + 10B)}}}
{{{10*(8 - B) + B + 18 = (8 - B) + 10B}}}
Simplify
{{{80 - 10B + B + 18 = 8 - B + 10B}}}
Combine like terms
{{{98 - 9B = 8 + 9B}}}
Add 9B to both sides
{{{98 = 8 + 18B}}}
Subtract 8 from both sides
{{{90 = 18B}}}
Divide both sides by 18
{{{highlight(5 = B)}}}
Now go back and use 5 for B and solve for A.
{{{A = 8 - B}}}
{{{A = 8 - (5)}}}
{{{highlight_green(A = 3)}}}