Question 1210504


given:

{{{a+3b=100}}}

{{{a}}} and {{{b}}} are positive {{{2}}} digest integers


Rearrange the equation to express {{{b}}} in terms of {{{a}}}: 

{{{b = (100 - 2a)/3}}}


 to ensure that {{{(100 - 2a)}}} is a positive integer which {{{highlight(requires)}}} {{{a<50}}}


Determine the range for {{{a}}}: 
since {{{a}}} must be a positive integer, ({{{1 < a < 50}}})


determine {{{b=(100 - 2a)/3}}}

check the {{{divisibility}}} {{{condition}}}: note {{{(100 - 2a)}}} {{{highlight(must)}}} be divisible by {{{3}}}

Count the valid integer values of {{{a}}} (knowing  that {{{a<50}}} ) which satisfy both conditions to find the total number of solutions.