The sum of two consecutive odd integers is 80.

Question

Write an equation to model this situation. Then find the larger integer

Answer 1

You may assign a variable to either of the integers, but it makes good sense to assign it to the value the problem asks you to find (so you won't forget to solve for it at the end).

 

Let x = larger odd integer

  then (x-2) is the smaller odd integer

 

Translate:

   "sum of two consecutive odd integers is 80"    means   (x-2) + x = 80

 

 2x -2 - 80

  2x = 82

   x = 41

 

Note:  the problem did not ask for the value of the smaller odd integer, but, to check, 39+41=80.

Answer 2

Let n = the smaller of the odd integers.  The next consecutive odd integer will be n+2 (because n+1 will be even, not odd).  The sum of the two consecutive odd integers equals 80:

 

n + (n+2) = 80

 

2n + 2 = 80

 

2n = 78

 

n = 39, n+2 = 41

Answer 3

n represents the first odd number

n + 2 represents the second odd number

 

n + n + 2 = 80       statement

2n + 2 = 80           combine like terms

2n = 78                 subtract 2 from both sides

n = 39

 

What is the other odd number?