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The sum of two consecutive even numbers is 270. What are the two numbers?

Mathematics

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Answer

134 and 136\text{}134 \text{ and } 136\text{}

Step-by-step solution

4 steps
  1. Define the two consecutive even numbers.

    Let the first even number be xx.
    Since the numbers are consecutive even numbers, the next even number will be x+2x+2.

  2. Set up the equation based on the given sum.

    The sum of the two numbers is 270:

    x+(x+2)=270x + (x+2) = 270
  3. Solve the equation for xx.

    Combine like terms:

    2x+2=2702x + 2 = 270

    Subtract 2 from both sides:

    2x=270−22x = 270 - 2 2x=2682x = 268

    Divide by 2:

    x=2682x = \frac{268}{2} x=134x = 134
  4. Find the two numbers.

    The first even number is x=134x = 134.
    The second consecutive even number is x+2=134+2=136x+2 = 134+2 = 136.

    The two numbers are 134 and 136\text{}134 \text{ and } 136\text{}.

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