The numbers are: 36 and 11 . ______________________________________________ Explanation: ______________________________________________ Let us represent the TWO (2) numbers with the variables; "x" and "y" . __________________________________________ x + y = 47 .
y − x = 25. __________________________________________ Since: " y − x = 25 " ;
Solve for "y" in terms of "x" ;
y − x = 25 ;
Add "x" to each side of the equation: _____________________________________________ y − x + x = 25 + x ;
to get:
y = 25 + x .
Now, since:
x + y = 47 ;
Plug in "(25 + x)" as a substitution for "y"; to solve for "x" :
x + (25 + x) = 47 ;
x + 25 + x + 47 ;
2x + 25 = 47 ;
Subtract "25" from each side of the equation:
2x + 25 − 25 = 47 − 25 ;
2x = 22 ;
Divide EACH SIDE of the equation by "2" ; to isolate "x" on one side of the equation; and to solve for "x" ;
2x / 2 = 22 / 2 ;
x = 11 ; ______________________________________________ x + y = 47<span> ;
</span>Plug in "11" for "x" into the equation ; to solve for "y" ;
11 + y = 47 ;
Subtract "11" from EACH SIDE of the equation; to isolate "y" on one side of the equation; and to solve for "y" ;
11 + y − 11 = 47 − 11 ;
y = 36 . ___________________________________________ So: x = 11 , y = 36 ; ___________________________________________ Let us check our work:
y − x = 25 ;
36 − 11 =? 25 ? Yes!
x + y = 47 ;
36 + 11 =? 47 ? Yes! ______________________________________________ The numbers are: 36 and 11 . ______________________________________________
