Question 216857
There are three consecutive odd integers. The middle integer is 116 less than three times the smallest integer. What are the three integers?


Step 1.  Let n be the smallest odd integer.


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


Step 3.  Let 3n be three times the smallest integer


Step 4.  Then n+2=3n+116 since middle integer is 116 less than three times the smallest integer


Step 5.  Solving the equation in Step 4 yields the following steps


{{{n+2=3n-116}}}


Add 116-n to both sides of the equation


{{{n+2+116-n=3n-116+116-n}}}


{{{118=2n}}}


Divide 2 to both sides of the equation


{{{118/2=2n/2}}}


{{{59=n}}}


Then {{{n+2=61}}} and {{{n+4=63}}}


Check middle integer....61=3*59-116=61...which is a true statement.


Step 6.  ANSWER:  The integers are 59, 61, and 63.


I hope the above steps were helpful. 


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And good luck in your studies!


Respectfully,
Dr J