Question 388997
Suppose the two numbers are x and y. Then, x+y = 27. From the second statement,

{{{x/2 + y/3 = 11}}}


Multiply the previous equation by 6 to clear the fractions (it makes life much easier...)


{{{3x + 2y = 66}}}. Rewrite 3x + 2y as x + 2x + 2y (so we can use substitution)


{{{x + 2x + 2y = 66}}} Since 2x + 2y = 54,


{{{x + 54 = 66}}}


x = 12. Substituting into the very first equation, we get y = 15.