SOLUTION: The product of two consecutive even numbers is 24. Find both pairs of numbers. Only an algebraic solution will be accepted.

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Question 855114: The product of two consecutive even numbers is 24. Find both pairs of numbers. Only an algebraic solution will be accepted.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Here is how to do this on your own.

Assign two variable expressions, one for each number. If you say, n is a Natural Number, the an EVEN number can be expressed generally as 2n. If you want two CONSECUTIVE even numbers, then the EVEN number which comes after 2n is 2n+2.

Understand clearly, you are NOT looking for two pair of numbers. You are looking for THE PAIR of numbers.

Return to the actual question: Find the pair of numbers? What pair? The product of two consecutive even numbers is 24. These numbers whose product is 24 are 2n and 2n+2. ...
... Do you know what to do?
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

The product of two consecutive even numbers is 24. Find both pairs of numbers. Only an algebraic solution will be accepted.


Let smaller of 2 numbers be S

Then larger = S + 2

Therefore, S(S + 2) = 24







Solve the quadratic for the 2 numbers. You should get smaller and larger being:

 or 

 

You can do the check!! 



If you need a complete and detailed solution, let me know!!



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