Question

1.

Find four consecutive odd integers such that the sum of the second and third is 19 grater
than the fourth.

Answer 1

Let
`2n+1` be the first integer. Then the next three odd integers are
`2n+3,2n+5,2n+7`

The sum of the second and third integers is 19 greater than the fourth, so that

`(2n+3)+(2n+5)=19+(2n+7)\implies2n=18\implies n=9`

Then the first integer is 19, and the four integers in question are 19, 21, 23, and 25.