Answer :
Answer:
60, 62, 64
Step-by-step explanation:
Let x, (x + 2) & (x+ 4) be three consecutive even integers.
[tex] \therefore \: x + (x + 2) + (x + 4) = 186 \\ \therefore \:3x + 6 = 186 \\ \therefore \:3x = 186 - 6 \\ \therefore \:3x = 180 \\ \therefore \:x = \frac{180}{3} \\ \therefore \:x = 60 \\ \implies \\ x + 2 = 60 + 2 = 62 \\ x + 4 = 60 + 4 = 64[/tex]
Hence, the three consecutive even integers are 60, 62 and 64.
Final answer:
To find three consecutive even integers whose sum is 186, we set up an equation and solve for the smallest integer. The result gives us the even integers 60, 62, and 64.
Explanation:
The sum of three consecutive even integers being 186 can be solved by setting up an algebraic equation. Let's denote the smallest even integer as x. Therefore, the next two consecutive even integers would be x+2 and x+4. The sum of these integers is given to be 186, so we write the equation x + (x+2) + (x+4) = 186. Simplifying this equation gives us 3x + 6 = 186. Subtracting 6 from both sides of the equation, we get 3x = 180. Dividing both sides by 3 results in x = 60. Therefore, the three consecutive even integers are 60, 62, and 64.
