Question 220990
The sum of two numbers is 56. The larger exceeds twice the smaller by 2. Find the numbers.

I already tried  x+2+2y = 56 with the substitution of x= 56-y


Good effort...I think you made the wrong substitution or equation


Step 1.  Let x be the smaller integer and y be the larger integer.


Step 2.  Then y=2x+2 since the larger exceeds twice the smaller by 2.


Step 3.   x+y=56 or x=56-y


Step 4.  Then substituting {{{x=56-y)}}} into {{{y=2x+2}}} yields the following


{{{y=2(56-y)+2}}}


{{{y=112-2y+2}}}


{{{y=114-2y}}}


Add 2y to both sides


{{{y+2y=114-2y+2y}}}


{{{3y=114}}}


Divide by 3 to both sides of the equation


{{{3y/3=114/3}}}


{{{y=38}}}


and {{{x=56-y=56-38=18}}}


Check equation if true in Step 2... 2*x+2=2*18+2=38...which is a true statement.


Step 5.  ANSWER:  The numbers are 18 and 38.


I hope the above steps were helpful.


For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


Good luck in your studies!


Respectfully,
Dr J