Final answer:
The problem is solved by defining the two unknowns with equations x - y = 8 and 5x + 4 = 71 - 4y. Through a process of substitution and simplification, the two numbers are determined to be 27 and 35.
Step-by-step explanation:
To solve this problem, let's start by defining the variables.
Let x be the larger number and y be the smaller number.
According to the problem, we know two things:
x - y = 8 and 5x + 4 = 71 - 4y.
These two equations will allow us to solve the problem using the method of substitution or elimination.
Let's rewrite the second equation by isolating 5x on one side: 5x = 67 + 4y.
Now we can substitute x from the first equation into this new form of the second equation, giving us: 5(y + 8) = 67 + 4y.
Expand and simplify to solve for y.
After simplification, we get: 5y + 40 = 67 + 4y, which simplifies further to y = 27.
Using y to find x, we have x = y + 8 = 27 + 8 = 35.
Therefore, the two numbers are 27 and 35.