Write a mathematical model for the problem and solve. The sum of two consecutive natural numbers is 505. Find the numbers.

Question

 I do not know how to do this problem. Can you please show me steps on how to answer a problem like this?

Answer 1

Alright, so we have two numbers. Let's call them a and b

Here's what we know:

a + b = 505 (these two numbers added together make 505)

b = a + 1 (since they're consecutive, that means one number is 1 larger than the other)

 

We now have a value for one of the variables, so we plug that into the equation:

a + (a + 1) = 505

combine like terms (the 'a's):

2a + 1 = 505

 

Subtract 1 from both sides:

2a + 1 - 1 = 505 - 1

2a = 504

 

Divide both sides by 2:

2a / 2 = 504 / 2

a = 252

 

Now that we have a, we can solve for b:

b = 252 + 1

b = 253

 

check our answer:

252 + 253 = 505

505 = 505

Answer 2

Let n be the lower of the 2 numbers.  Then the other number must be n + 1 (consecutive).  The sum of the 2 is 505.  Therefore,

 

n + (n + 1) = 505

 

2n + 1 = 505

 

n = (505 - 1) / 2 = 504/2 = 252

 

The 2 numbers are 252 and 253.