Question 220978
Find three consecutive odd integers such that the sum of the first, two times the second, and three times the third is 82.


Step 1.  Let n be one odd integer.


Step 2.  Let n+2 and n+4 be the next two odd consecutive integer.


Step 3.  Let 2(n+2) be two times the second.


Step 4.  Let 3(n+4) be three times the third.


Step 5.  Then n+2(n+2)+3(n+4)=82 since the sum of the first, two times the second, and three times the third is 82


Step 6.  Solving n+2(n+2)+3(n+4)=82  yields the following steps.


*[invoke explain_simplification "n+2(n+2)+3(n+4)=82" ]

{{{n=11}}} {{{n+2=13}}} and {{{n+4=15}}}


Check sum...11+2*13+3*15=11+26+45=82... which is a true statement


Step 7.  ANSWER:  The three consecutive odd integers are 11, 13, and 15.


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