Question 403924


The apartments in Vincent's apartment house are numbered consecutively on each floor. The sum of his next door neighbor's number is 2409. What are the numbers?


Remember, consecutive numbers follow the form: x, x+1, x+2, etc...



So because "The apartments in Vincent's apartment house are numbered {{{consecutively}}} on each floor", this means that Vincent's apartment number is {{{either}}}{{{ one}}}{{{ more }}}{{{or }}}{{{one}}}{{{ less}}} than her neighbors.


Let's make {{{x = Vincent's_ number}}}


and let's make his neighbor be one more, which means that {{{x+1=neighbor's _number}}}


Now since "The sum of his number and his next door neighbors number is 2409", this tells us that 


Vincent's Number + Neighbor's Number = 2409



which also looks like



{{{x+(x+1) = 2409}}}

let's solve for "x":



{{{x+(x+1)=2409}}} .........the given equation...



{{{2x+1=2409}}} Combine like terms.



{{{2x=2409-1}}} Subtract {{{1}}} from both sides.



{{{2x=2408}}} Combine like terms on the right side.



{{{x=(2408)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x= 1204}}} 


So, the answer is {{{x=1204}}} 



This means that Vincent's house number is 1204  and his neighbor's is 1205.

check:


{{{1204+1205=2409}}}