Another type of number problem involves consecutive numbers. Consecutive numbers are numbers that come one after the other, such as 3, 4, 5. If we are looking for several consecutive numbers it is important to first identify what they look like with variables before we set up the equation. This is shown in the following example. Example The sum of three consecutive integers is `93`. What are the integers?

`x`	Make the first number `x`
`x+1`	To get the next number we go up one or+1
`x+2`	Add another 1 (2 total) to get the third
`(x)+(x+1)+(x+2)=93`	Add three parts equals 93
`x+x+1+x+2=93`	Here the parenthesis aren′t needed.
`3x+3=93`	Combine like terms
`3x+3color(red)(-3)=93color(red)(-3)`
`3x=90`
`(3x)/color(red)(3)=90/color(red)(3)`
`x=30 `

First integer: 30 Second integer: 31 Third integer: 32 Sometimes we will work consecutive even or odd integers, rather than just consecutive integers. With even or odd numbers they are spaced apart by two. Example The sum of three consecutive even integers is `246`. What are the numbers?

`x`	Make the first number `x`
`x+2`	Even numbers, so we add 2 to get the next
`x+4`	Add another 2 (4 total) to get the third
`(x)+(x+2)+(x+4)=246`	Add three parts equals 246
`x+x+2+x+4=246`
`3x+6=246`
`3x+6color(red)(-6)=246 color(red)(-6)`
`3x=240`
`(3x)color(red)(3)=240/color(red)(3)`
`x=80`

First integer: 80 Second integer: 82 Third integer: 84 Example Find three consecutive odd integers so that the sum of twice the first, the second and three times the third is 152.

`x`	Make the first x
`x+2`	Odd numbers so we add 2
`x+4`	Add 2 more (4 total) to get the third
`2(x)+(x+2)+3(x+4)`	The sum of twice the first, the second and three times the third
`2(x)+(x+2)+3(x+4)=152`	is 152
`2x+x+2+3x+12=152`	Distribute through parenthesis
`6x+14=152`	Combine like terms
`6x+14color(red)(-14)=152color(red)(-14)`
`6x=138`
`(6x)/color(red)(6)=138/color(red)(6)`
`x=23`

First integer: 23 Second integer: 25 Third integer: 27