Final answer:
To solve the problem, we set up an equation where the smaller consecutive even number is expressed as the product of the larger number and ten, minus seventy-four. After simplifying the equation, we find that the two consecutive even numbers are 6 and 8.
Step-by-step explanation:
The student asked to find two consecutive even numbers where the smaller number is seventy-four less than the product of the larger number and ten. We can start by defining the larger even number as x, which makes the smaller even number x-2, as they are consecutive even numbers. The problem gives us the equation x-2 = 10x - 74. Simplifying this equation:
- Move all terms involving x to one side: x - 10x = -74 + 2
- Combine like terms: -9x = -72
- Divide by -9 to find x: x = 8
Since x is the larger number, the two consecutive even numbers are 6 and 8.