Answer:
[tex]6[/tex], [tex]8[/tex] and [tex]10[/tex]
Step-by-step explanation:
Let [tex]x =[/tex] smallest consecutive even integer.
Since the second and third consecutive even integers can be expressed by our smallest even consecutive integer, we can express them as:
Second consecutive even integer = [tex]x+2[/tex]
Third consecutive even integer = [tex]x+4[/tex]
From "the sum of the second and third is 3 times the first integer", we can write:
[tex]x+2+x+4 = 3x[/tex]
[tex]2x+6 = 3x[/tex] (collect like-terms)
[tex]x=6[/tex]
∴ The first consecutive even integer is 6
Now, we can use substitution to find the values of the second and third consecutive even integers:
Second consecutive integer = [tex]x+2[/tex]
[tex]=6+2[/tex]
[tex]=8[/tex]
Third consecutive integer = [tex]x+4[/tex]
[tex]=6+4[/tex]
[tex]=10[/tex]
∴ The three consecutive even integers are [tex]6[/tex], [tex]8[/tex] and [tex]10[/tex].
Hope this helps :)
