find three consecutive integers such that the sum of the integers plus four is equal to four times the second integer

Question

I have to

1. represent each integer with an unknown

 

2.write an equation using the unknowns

 

3.solve for three integers

 

4. check by substituting the integers in the equation

Answer 1

Hi Leah,

 

We know that we have three consecutive integers, so we could represent those unknown integers as:

 

    x

 

    x+1

 

    x+2

 

The problem tells us that the "sum" (addition) of those three integers plus four is equal to four times the second integer. We can represent this with an equation:

 

    x + (x+1) + (x+2) + 4 = 4*(x+1)         (because "x+1" is the second integer)

 

Combining the like terms, and distributing:

 

    x + x + x + 1 + 2 + 4 = 4x + 4

 

    3x + 7 = 4x + 4

 

Now we can solve for "x", which is our first integer:

 

    3x + 7 = 4x + 4

   -3x         -3x

 

    7 = x + 4

   -4        -4

 

    3 = x

 

Since the first integer is 3, the other two are 4 and 5.

 

To check, we will plug these values back into our equation:

 

    3 + 4 + 5 + 4 = 4*4

 

    16 = 16, so our solution is correct.

 

I hope this helps!