SOLUTION: 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?

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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?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

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%27s_+number

and let's make his neighbor be one more, which means that x%2B1=neighbor%27s+_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%2B%28x%2B1%29+=+2409
let's solve for "x":


x%2B%28x%2B1%29=2409 .........the given equation...


2x%2B1=2409 Combine like terms.


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


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


x=%282408%29%2F%282%29 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%2B1205=2409