Question

Eight consecutive odd integers are arranged in ascending order, from smallest to largest. The sum of the last four integers is 232. What is the sum of the first four integers?

Answer 1

Answer: The sum of the first four integers is 200.

Explanation:

Let x be the smallest odd integer, then the other seven integers will be
`x+2,x+4,x+6,x+8,x+10,+12\ and\ x+14`

The sum of the first four integers=
`x+(x+2)+(x+4)+(x+6)=4x+12`

The sum of the last four integers is 232.

`\\\Rightarrow\ x+8+x+10+x+12+x+14=232\\\Rightarrow\ 4x+44=232\\\Rightarrow\ 4x=188\\\Rightarrow\ x=47`

Now, sum of the first four integers=
`4(47)+12=188+12=200`