Answer:
6, 8, 10
Step-by-step explanation:
Consecutive even integers are in the form:
2, 4, 6 ... etc
As we can see, they have a "gap" of 2 in between. Thus, if we let the first number be "x", the next consecutive even number would be "x + 2" and the next one would be "x + 4".... and so on...
We have our numbers: x, x + 2, x + 4
It says the sum of twice the smallest and 3 times the largest is 42. We can write:
[tex]2x + 3(x+4) = 42[/tex]
This is the equation. Now we solve for x and find all the 3 consecutive even integers. Shown below:
[tex]2x + 3(x+4) = 42\\2x + 3x + 12 = 42\\5x = 42 - 12\\5x = 30\\x = \frac{30}{5}\\x=6[/tex]
The 3 integers are 6, 8, and 10
