The difference between the two numbers is 8 and the sum of these numbers is 14.

The difference between the two numbers is 8 and the sum of these numbers is 14. Find the product of twice the second number and half of the first.

Let the first number be denoted by x, and the second by y.
Considering the condition of the problem, we compose a system of equations.
x-y = 8;
x + y = 14;
To solve the system of equations, we use the substitution method.
We express in the first equation the variable x through y.
x = y + 8;
x + y = 14;
Substitute the expression for x in the second equation.
y + 8 + y = 14;
We transfer the known term of the equation to the right side while changing its sign to the opposite.
2y = 6;
y = 6: 3;
y = 3;
x = 3 + 8 = 11;
Let’s write an expression whose value you want to find by the condition of the problem.
2y * 1 / 2x = 2 * 3 * 1/2 * 11 = 6 * 11/2 = 33.
Answer: 33.