The sum of three consecutive odd integers is 89 less than twice the largest integer.

[sean1]

Hello,
I am trying to catch up homework this weekend but this has me stumped because I do not feel like I solved this one correctly. Could someone please check my work for me? I will try to include the work I did the best as possible. Than you

Problem from textbook:

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

My best attempt:

x+(x+2)+(x+4) = 2(x+4)-89
3x+6 = 2x+8-89
3x=2x-87
x= -87
x+2 = -85
x+4 = -83

This just doesnt seem write to me. If anybody could help I would appreciate it. Thanks!

 

[ksdhart2]

Well, all the steps you've taken look fine to me. And if you're ever uncertain about an answer, you can always check it yourself by plugging it in and seeing if it meets the requirements of the problem. Let's start with the given:

\(\displaystyle x+(x+2)+(x+4)=2(x+4)-89\)

Plug in x = -87:

\(\displaystyle -87+(-87+2)+(-87+4)=2(-87+4)-89 \implies -87-85-83=2(-83)-89 \implies -255=-166-89 \implies -255=-255\)

The equation holds true, so your answer is correct. And -87 is an odd integer (the problem text never specified it had to be positive), so that checks out as well.

 

[sean1]

Well, all the steps you've taken look fine to me. And if you're ever uncertain about an answer, you can always check it yourself by plugging it in and seeing if it meets the requirements of the problem. Let's start with the given:

\(\displaystyle x+(x+2)+(x+4)=2(x+4)-89\)

Plug in x = -87:

\(\displaystyle -87+(-87+2)+(-87+4)=2(-87+4)-89 \implies -87-85-83=2(-83)-89 \implies -255=-166-89 \implies -255=-255\)

The equation holds true, so your answer is correct. And -87 is an odd integer (the problem text never specified it had to be positive), so that checks out as well.

Great tip, I will remember that one. Thank you so much for your help!