Final answer:
To solve this word problem, we need to set up an equation and solve it. The two consecutive even integers are 6 and 8.
Step-by-step explanation:
To solve this word problem, we need to set up an equation based on the given information. Let's call the first even integer 'x' and the second even integer 'x+2'. The problem tells us that the product of these two numbers is 18 more than 5 times the first integer, so we can write the equation as: x(x+2) = 5x + 18.
To solve this equation, we can simplify and rearrange it: x^2 + 2x = 5x + 18. Moving all the terms to one side, we get: x^2 - 3x - 18 = 0. Factoring or using the quadratic formula, we find that x = 6 or x = -3.
Plugging these values back into the original equation, we find that x = 6 gives us a valid solution, while x = -3 does not. Therefore, the two consecutive even integers are 6 and 8.