The sum of two consecutive even numbers is 174. Find the smaller number.
Correct Answer :
86
Solution :
To find the smaller of two consecutive even numbers whose sum is 174, we can set up a simple algebraic equation.
Let the smaller even number be represented by .
Since consecutive even numbers differ by 2, the next consecutive even number (the larger one) will be .
According to the problem, the sum of these two consecutive even numbers is 174. We can write this relationship as:
Now, we simplify the equation by combining like terms:
Subtract 2 from both sides of the equation to isolate the term with :
Divide both sides by 2 to solve for :
Thus, the smaller even number is 86. (The larger consecutive even number would be , and their sum is indeed ).
Therefore, the correct option is 86.
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