College Algebra word problem

Question

The sum of the two smallest of five consecutive even integers is 50 less than the sum of the other integers. What is the smallest integer?

Answer 1

Let x = the smallest integer. All subsequent integers are (x+2), (x+4), etc.

 

The sum of the two smallest: x + (x+2) = 2x + 2

The sum of the rest: (x+4) + (x+6) + (x+8) = 3x + 18

 

Since the sum of the two smallest is 50 less than the other, we can write the equation as follows:

 

2x + 2 = (3x+18) - 50, then simplify

 

2x + 2 = 3x - 32 (combine like terms)

34 = x (isolate variable)

 

Therefore, the smallest integer is 34. 

 

Answer 2

Let x=smallest integer     (since the problem asks us to find it)

 

The other four consecutive even integers are:   x+2, x+4, x+6, and x+8

 

Translate "The sum of the two smallest of five consecutive even integers is 50 less than the sum of the other integers."

     (x) + (x+2) = -50 + [(x+4) + (x+6) + (x+8)]

       2x + 2 = 3x -32              (collect terms)

          34 = x 

 

The five even integers are:  34, 36, 38, 40, 42

 

Checking (very important):

  Is  34+36 = (38+40+42) - 50     ?

          70   =  70    ?   yes