Question #bacf0

1 Answer
Dec 27, 2017

7, 9, 11, and 13

Explanation:

Let the consecutive odd integers be x, x+2, x+4, and x+6

Even numbers are added to x because of the assumption that x is an odd integer and we need to add 2 to get the next odd integer. for example, if x=3, then we need to add 2 to 3 to get the next odd integer which is 5 and so on. Adding 1 will make the next number even.

Now, make and equation to match the condition given in the question,

x+ (x+4) = 1/2 {(x+2)+(x+6)}+7

or, 2x +4 = 1/2(2x+8)+7

or, 2x+4 =(x+4)+7
On the right side when 1/2 is multiplied to 2x, both the twos get cancelled and only x remains. Similarly, 4 remains after 1/2 is multiplied to 8.

So, now the equation becomes:
2x+4 = x+11 (Note: 4+7 = 11)

Solving for x,
2x-x = 11=4
or, x = 7

Therefore, other consecutive odd numbers are:
x+2 = 7+2=9
x+4 = 7+4 = 11
and,
x+6 = 7+6 = 13