Question 214750
One-sixth of the smallest of three consecutive even integers is three less than one-tenth the sum of the other even integers.  Find the integers.


Step 1.  Let x be an even integer, x+2 and x+4 be the next two consecutive integers.


Step 2.  x+2+x+4 is the sum of the two even integers or 2x+6

Step 3.  (2x+6)/10 is one-tenth of the sum of the other even integers.


Step 4.   x/6 is one-sixth of the smallest even itneger


Step 5.   {{{x/6=(2x+6)/10-3}}}  as given by the problem statement.


Step 6   Multiply 60 to both sides of the equation to get rid of the fractions.


{{{60*x/6=60*((2x+6)/10-3)}}}


{{{10x=6*(2x+6)-180}}}


{{{10x=12x+36-180}}}


{{{10x=12x-144}}}


Add 144-10x to both sides


{{{10x+144-10x=12x-144+144-10x}}}


{{{2x=144}}}


{{{x=72}}}


Step 7.  The numbers are 72, 74 and 76.


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J