Question 96237
Since {{{2x}}} refers to any even number, {{{2x+1}}} refers to any odd number. So the sum of three consecutive odd numbers is:


{{{(2x+1)+(2x+3)+(2x+5)}}}




{{{(2x+1)+(2x+3)+(2x+5)=105}}} Start with the translated equation




{{{(2x+2x+2x)+(1+3+5)=105}}} Group like terms on the left side


{{{6x+9=105}}} Combine like terms on the left side



{{{6x=105-9}}}Subtract 9 from both sides



{{{6x=96}}} Combine like terms on the right side



{{{x=(96)/(6)}}} Divide both sides by 6 to isolate x




{{{x=16}}} Reduce

      



Now plug in {{{x=16}}} into {{{2x+1}}}



{{{2(16)+1=32+1=33}}}



So the first number is 33


Now plug in {{{x=16}}} into {{{2x+3}}}


Second Number:


{{{2(16)+3=32+3=35}}}


Now plug in {{{x=16}}} into {{{2x+5}}}

Third Number:


{{{2(16)+5=32+5=37}}}


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Answer:


So the three numbers are 33,35, and 37