The sum of three consecutive odd integers is 89 more than twice the largest integer. Find the Integers.

Question

I do not know how to set up this word problem. 

Answer 1

The odd integers can be written as 2n+1 where n=0,1,2,.... so three consecutive odd integers can be written as

 

2n+1, 2(n+1)+1, 2(n+2)+1 and we were told that the sum of these is equal to 89+4(n+2)+2 so now we have,

combining like terms and doing the arithmetic, 2n=90or n=45. so the integers are 91,93 & 95

 

Jim

Answer 2

Sarah,

 

Let our 1st odd integer = x, then the 2nd will be x+2, and the 3rd will be x+4

 

Now the sum is twice the largest, i.e. 2(x+4) plus 89, so

 

x + (x+2) + (x+4) = 89 + 2(x+4)

 

3x + 6 = 89 +2x + 8 ⇒ 3x - 2x = 89 + 8 - 6 ⇒

 

x = 91

 

so our three consecutive integers are:  91, 93, 95 which sum to 91 + 93 +95 = 279

 

we test out solution:  89 + 2(95) = 89 + 190 = 279!