Question

What four consecutive integers have a sum of 26?

Answer 1

`color(blue)(5 + 6 +7+ 8 = 26")`

Explanation:

Let the first number be `n`

Then the four consecutive numbers are:

`n" ; "(n+1)" ; "(n+2)" ; "(n+3)`

So :`" "n+(n+1)+(n+2)+(n+3) = 26`

`=>4n+6=26`

Subtract 6 from both sides

`=>4n+6-6=26-6`

`4n+0=26-6" "`

`color(brown)("Notice that the above is the source method that gives the shortcut")`
`color(brown)("approach. Which is: for add and subtract, move it to the other side")`
`color(brown)("of the = and change the sign.")`

Divide both sides by 4

`4/4xxn=20/4`

But `4/4=1`

`n=5`

`color(brown)("Notice that the above is the source method that gives the shortcut")`
`color(brown)("approach. Which is: for multiply, move it to the other side")`
`color(brown)("of the = and divide by it. For divide, move it to the other side")`
`color(brown)("of the = and change it to multiply")`

If the first number is 5 then the numbers are:

`color(blue)(5 + 6 +7+ 8 = 26")`