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?

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) (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 on each floor", this means that Vincent's apartment number is

than her neighbors.

Let's make

and let's make his neighbor be one more, which means that

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

let's solve for "x":

.........the given equation...

Combine like terms.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

So, the answer is

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

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