SOLUTION: the sum of 4 consecutive odd integers is 216. solve the equation to determine the smallest integer.

Algebra ->  Conversion and Units of Measurement -> SOLUTION: the sum of 4 consecutive odd integers is 216. solve the equation to determine the smallest integer.      Log On


   

Question 155747: the sum of 4 consecutive odd integers is 216.
solve the equation to determine the smallest integer.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Consecutive odd integers follow the pattern: 2x%2B1, 2x%2B3, 2x%2B5, 2x%2B7, etc...


So if "the sum of 4 consecutive odd integers is 216", then this means that the equation is 2x%2B1%2B2x%2B3%2B2x%2B5%2B2x%2B7=216


2x%2B1%2B2x%2B3%2B2x%2B5%2B2x%2B7=216 Start with the given equation.


8x%2B16=216 Combine like terms on the left side.


8x=216-16 Subtract 16 from both sides.


8x=200 Combine like terms on the right side.


x=%28200%29%2F%288%29 Divide both sides by 8 to isolate x.


x=25 Reduce.


2x%2B1 Go back to the first number (which is the smallest integer of the four)


2%2825%29%2B1 Plug in x=25


50%2B1 Multiply


51 Add


----------------------------------------------------------------------

Answer:

So the smallest integer of the group is 51




Check:

51+53+55+57=216

216=216 ... works