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

Question

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

Answer 1

Let x = the smallest of the consecutive even integers.  The others are x+2, x+4, x+6, and x+8.  The sum of the two smallest of five consecutive even integers ( x + x+2) is (=) 50 less (-50) than the sum of the other three integers (x+4 + x+6 + x+8):

 

x + x+2 = x+4 + x+6 + x+8 - 50

 

Combine like terms:

 

2x + 2 = 3x - 32

 

Solve for x.