Question

The sum of two consecutive odd integers is 189. Find the integers.​

Answer 1

Answer:

What three consecutive integers have a sum of 189? Which means that the first number is 62, the second number is 62 + 1 and the third number is 62 + 2. Therefore, three consecutive integers that add up to 189 are 62, 63, and 64.

Answer 2

Answer:

An odd number take the form:

2

k

+

1

Hence the next odd numbers must

2

k

+

3

and

2

k

+

5

Sum means to add together:

(

2

k

+

1

)

+

(

2

k

+

3

)

+

(

2

k

+

5

)

=

189

Colect like terms:

⇒

6

k

+

9

=

189

⇒

6

k

=

180

⇒

6

k

6

=

180

6

⇒

k

=

30

⇒

2

k

+

1

=

(

2

⋅

30

)

+

1

=

61

Hence the odd numbers are

61

,

63

,

65