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):
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. ...
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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!!
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