The sum of the two numbers is 65, and the sum of 37% of the first number and 28%

The sum of the two numbers is 65, and the sum of 37% of the first number and 28% of the second is 21.53. What is the product of these numbers?

Let us denote the required numbers by x and y.
According to the condition of the problem, the sum of 37% of the first number and 28% of the second number is 21.53, therefore,
0.37 * x + 0.28 * y = 21.53.
It is also known that the sum of these two numbers is 65, therefore,
x + y = 65.
We solve the resulting system of equations.
We multiply both sides of the second equation but 0.37 and subtract from the first equation:
0.37 * x + 0.28 * y – 0.37 * x – 0.37 * y = 21.53 – 65 * 0.37;
-0.09 * y = -2.52;
0.09 * y = 2.52;
y = 2.52 / 0.09;
y = 28.
Knowing y, we find x:
x = 65 – y = 65 – 28 = 37.
We find the product of these numbers:
37 * 28 = 1036.
Answer: The product of these numbers is 1036.