SOLUTION: If the first and third of three consecutive odd intergers are added, the result is 51 less than five times the second interger. Find the third interger. Can you please show me

Question 354951: If the first and third of three consecutive odd intergers are added, the result is 51 less than five times the second interger. Find the third interger.
Can you please show me step-by step so I understand how to find the answer on the rest of my homework?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let the integers be x,x+2,x+4
the differenc between odd integers is 2
so if the first integer is x then the next will be x+2
the third will be x+2+2=x+4
..
the sum of first & the third are x+x+4 =2x+4
5 times the second integer = 5(x+2)
51 less than 5 times the second = 5(x+2)-51
they are equal
x+x+4 = 5(x+2)-51
2x+4 = 5x+10-51
2x+4 = 5x-41
add -4
2x+4-4 = 5x-41-4
2x=5x-45
add -5x to both sides
2x-5x=5x-5x-45
-3x=-45
divide by -3
-3x/-3= -45/-3
x=15 the first integer
the second will be x+2 = 15+2
the third will be x+4 = 15+4=19
...
the odd integers are 15,17,19
...
C H E C K
15+17+19=51
...
m.ananth@hotmail.ca
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