Question

The sum of two consecutive odd integers is 132. What are the two integers?

Answer 1

65 and 67

Explanation:

we can represent even numbers as 2n where n is an integer

so odd integers can be represented as 2n+1

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

so we can represent the 2 odd consecutive integers as 2n+1 and 2n+3

their sum is 132

(2n+1)+(2n+3)=132

expand

2n+1+2n+3=132

4n+4=132

minus 4 from both sides

4n=128

divide both sides by 4

n=32

the numbers are 2n+1 and 2n+3

2n=2*32=64

2n+1=64+1=65

2n+3=64+3=67

the 2 integers are 65 and 67

Answer 2

65 and 67

Explanation:

two consecutive odd numbers would look like this:

x and x + 2

this is because of how counting numbers works:

1 2 3 4 5 6 7

the consecutive numbers here would be 1, 3, 5, 7, etc.

if one number (x) was 1, the next number would be (x + 2) which is three. This formula will work for all consecutive odd numbers.

so, x + x + 2 = 132

2x + 2 = 132

-2 -2

2x = 130

/2 /2

x = 65

the first number is x = 65

the second number is x + 2 which means this number is 65 + 2 = 67

(check: 65 + 67 = 132)