SOLUTION: Write a word problem about consecutive integers that can be solved using the equation x+x+2+x+4=78 Solve the equation . Explain what your answer means about your wor problem.

Question 987206: Write a word problem about consecutive integers that can be solved using the equation x+x+2+x+4=78
Solve the equation . Explain what your answer means about your wor problem.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Just looking at the LHS, you know that you either have three consecutive odd integers or three consecutive even integers. That is because if you start with an odd integer

, then the integer two larger and the integer four larger both must be odd. Likewise, all three must be even if you start with an even integer.

However, looking at the RHS, we see that we have a set of three consecutive even integers. Since it is impossible for the sum of three odd integers to be even, and I will leave verification of this assertion as an exercise for the student, the three integers must be even and since the common difference is two, they must be consecutive.

You can make up as complicated a story as you like so long as the bottom line is: "the sum of three consecutive even integers is 78".

You can solve the equation for yourself. The solution to the equation is the value of

. If you are careful about how you define the meaning of your variables, either in your problem statement or in the introduction to your solution, the answer to your last question will be obvious.

John

My calculator said it, I believe it, that settles it

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