Question

The sum of 7 consecutive numbers is 105. What are the numbers? Please show how to do it and steps!

Answer 1

Since they are consecutive, we can write that (x = the first number):

$(x)+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)+(x+6) = 105$

Let's simplify:

$7x+21 = 105$

Solve for x:

$7x = 84$

$x = 12$

That's the first number which means the numbers are the 7 numbers which follow: 12, 13, 14, 15, 16, 17, 18.

To check, sum of those is:

$12+13+14+15+16+17+18 = 105$

So, it all works out! Your answer is: 12, 13, 14, 15, 16, 17, 18.

Answer 2

We need to create an equation in order to solve this problem.

Let x = the smallest number

x+1 = next  number

x+2 the following number

x+3

x+4

x+5

x+6

So, we add those.

x+x+1+x+2+x+3+x+4+x+5+x+6=105

7x+21=105

7x = 84

x = 12

So the numbers are

12,13,14,15,16,17,18