SOLUTION: Hi I am stumped on this problem as well. We have to have 2 equations and use the HES method to solve this problem. Here is the question: Find two consecutive odd integers whose su

Question 540673: Hi I am stumped on this problem as well. We have to have 2 equations and use the HES method to solve this problem. Here is the question:
Find two consecutive odd integers whose sum is 168.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I have no idea what your teacher or textbook calls the HES method. As a matter of fact, I do not like the idea of memorizing problem solving recipes at all. I believe in understanding and remembering a few basic concepts, and using logical thinking to get from that to a solution, if allowed.
Even further, I think algebra is wasted on this problem. Consider the number (expected to be even) in between those two consecutive odd numbers. One of your odd numbers is one less that the middle number, and the other odd number is one more that the middle number. As a consequence, their sum is twice that middle number. So the middle number must be 84 and the two consecutive odd numbers must be 83 and 85. Mental math?
If I had to write one equation, it would be , calling the two consecutive odd numbers n and n+2. That does not reflect the fact that the numbers are odd, but there are only 2 numbers with a difference of 2 that add up to 168, and once we find them we can verify that they are odd. If they weren't, there would be no solution to the problem.
To reflect the fact that they are odd, I could say that the numbers are
and , which would simplify to
That would give you two equations, but then you would need
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