word problem help?

Question

two times the sum of three consecutive odd integers is the same 23 more than 5 times the largest integer. find the integers.

Answer 1

Let the smallest odd integer be X.  Then the next 2 consecutive odd integers are (X+2) and (X+4).  

 

"2 times the sum" is 2*(X + X+2 + X+4) = 2*(3X + 6) = 6X + 12

 

"23 more than 5 times the largest" is 5*(X+4) + 23 = 5X + 20 + 23 = 5X + 43  

 

These 2 expressions are the same, so  

 

6X + 12 = 5X + 43

X = 31

 

So the 3 consecutive odd integers are 31, 33 and 35  

 

Check:  2 times the sum is 2*(31 + 33 + 35) = 2*(99) = 198

            5 times the largest is 5*35 = 175.  

            198 is 23 more than 175