Question

The sum of two consecutive positive odd integers is two hundred sixty-four. find the two integers.

Answer 1

odd integers are 2 apart (1,3,5,7, etc)

odd integers can be reprsented in the form 2n+1 or 2n-1 where n is an integer

so 2 consecutive integers can be represented as 2n-1 and 2n+1 (2 apart)

their sum (add) is 264

2n-1+2n+1=264

4n=264

divide both sides by 4

n=66

the numbers are 2n-1 and 2n+1

2n-1=2(66)-1=132-1=131

2n+1=2(66)+1=132+1=133

the 2 integers rae 131 and 133

Answer 2

Any integer (not a fraction) that cannot be divided exactly by 2 is an odd integer.

So, we have ( 2k + 1 ) + ( 2k + 3 ) = 264, where 2k + 1 and 2k + 3 are the two consecutive positive odd integers ( k > 0 );

Then, 4k + 4 = 264;

4k = 260;

k = 65;

2k + 1 = 131;

2k + 3 = 133;

The chosen numbers are 131 and 133.