Find four consecutive integers whose sum is 114

Question

I need help please

Answer 1

Let x be the first number of the four.

 

so the first number is x

the next consecutive number is only 1 more than the first number so: x+1

the third number will be two away from the first so: x +2 

the fourth number will be x+3

 

so our 4 numbers we are looking for can be represented as follows:

x

x+1

x+2

x+3

 

to make sure this is correct pick any number for x and plug it in. 

 

You will get four consecutive numbers.

 

We know that the sum of these numbers adds up to 114 so we can make an equation with that.

 

x + (x+1) + (x+2) + (x+3) = 114

 

now combine like terms and solve for x

 

4x + 6 = 114

4x = 108

x = 27

 

so the first number is 27 and the rest are 28, 29, and 30.

 

to check and make sure add the numbers and they should equal 114

Answer 2

A trick to this is using algebra. Since you are trying to find four consecutive integers... the first one will be X. the next will x+1 and so on and so forth. You would then simplify your equation and it would be 4x+6(x, x+1, x+2, x+3)and then you will set it equal to 114 and solve. Hope this helps?