Question

The number 15 can be written as the sum of consecutive numbers (numbers in a row).There are 3 ways.

Answer 1

You have to determine wich consecutive numbers can be added to give 15 as a result. (Whole numbers)

a.

Let x be the first number and x+1 be the consecutive number.

If you add them the result should be 15:

`\begin{gathered} x+x+1=15 \\ 2x+1=15 \\ 2x=15-1 \\ 2x=14 \\ (2x)/(2)=(14)/(2) \\ x=7 \end{gathered}`

The first number is 7 and the consecutive number is x+1=7+1=8

So the first consecutive numbers that add up to 15 are

`7+8=15`

b. Now you have to find 3 consecutive numbers that add up to 15.

Let "x" be the smaller number, the next number will be "x+1" and the third number will be "x+2"

Add them up:

`\begin{gathered} x+(x+1)+(x+2)=15 \\ x+x+1+x+2=15 \\ 3x+3=15 \\ 3x=15-3 \\ 3x=12 \\ (3x)/(3)=(12)/(3) \\ x=4 \end{gathered}`

The first number is x=4, then the next number is x+1=4+1=5, and the third one will be x+2=4+2=6.

The three consecutive numbers that add up to 15 are:

`4+5+6=15`

c. Finally you have to find 5 consecutive numbers that add up to 15. Following the same method as before, the first number will be represented by "x", then the following numbers will be "x+1", "x+2", "x+3" and "x+4"

`\begin{gathered} x+(x+1)+(x+2)+(x+3)+(x+4)=15 \\ 5x+10=15 \\ 5x=15-10 \\ 5x=5 \\ (5x)/(5)=(5)/(5) \\ x=1 \end{gathered}`

The 5 consecutive numbers that add up to 15 are

`1+2+3+4+5=15`