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

User Dagalpin
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2 Answers

3 votes

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.

User Cherrylyn
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7.7k points
3 votes

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

User Miloss
by
8.6k points

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