Find three consecutive even integers such that the sum of the least integer and the middle integer is 3636 more than the greatest integer
Mathematics · High School · Thu Feb 04 2021
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Let's denote the three consecutive even integers as follows:
- The least integer: x - The middle integer: x + 2 (since even integers are two units apart) - The greatest integer: x + 4 (two more than the middle one)
According to the problem, we're told that the sum of the least integer and the middle integer is 3636 more than the greatest integer. Therefore, we can set up the following equation:
x + (x + 2) = (x + 4) + 3636
Now let's solve the equation step by step:
2x + 2 = x + 4 + 3636 2x + 2 = x + 3640 2x - x = 3640 - 2 x = 3638
Now that we've solved for x, we can find the three consecutive even integers:
- The least integer: x = 3638 - The middle integer: x + 2 = 3638 + 2 = 3640 - The greatest integer: x + 4 = 3638 + 4 = 3642
So the three consecutive even integers are 3638, 3640, and 3642.