Question 715216
{{{a}}} = tens digit
{{{b}}} = units digit
The value of the number is {{{10a+b}}}
 
"The sum of the digits of a two digit number is ten" translates as
{{{a+b=10}}}
 
"The original number is two more than five times the units digit" translates as
{{{10a+b=5*b+2}}} --> {{{10a+b=5b+2}}} --> {{{10a+b-5b=5b+2-5b}}} --> {{{10a-4b=2}}}
 
We need to solve the system {{{system(a+b=10,10a-4b=2)}}}
we can solve the first equation for {{{a}}} and substitute the expression found for {{{a}}} in the second equation to find {{{b}}}
{{{a+b=10}}} --> {{{a=10-b}}}
{{{10a-4b=2}}} --> {{{10(10-b)-4b=2}}} --> {{{100-10b-4b=2}}} --> {{{100-14b=2}}} --> {{{100-14b+14b-2=2+14b-2}}} --> {{{100-2=14b}}} --> {{{98=14b}}} --> {{{98/14=14b/14}}} --> {{{highlight(b=7)}}}
Now we substitute that value into one of the equations to find {{{a}}} :
{{{a+b=10}}} --> {{{a+7=10}}} --> {{{a=10-7}}} --> {{{highlight(a=3)}}}
The number is {{{highlight(37)}}}