7) The sum of two nombers is 50 , their prodect is a maximum Algebraically datermine the two numbers. (3 marks)

Step 1 ：Let the two numbers be x and y, such that x + y = 50

Step 2 ：Express y as (50 - x)

Step 3 ：Find the maximum product P = x * (50 - x)

Step 4 ：Differentiate P with respect to x: dP/dx = 50 - 2x

Step 5 ：Find the critical points: 50 - 2x = 0, x = 25

Step 6 ：The maximum product is P = 25 * (50 - 25) = 625

Step 7 ：\( \boxed{\text{Final Answer: The two numbers are 25 and 25, and their maximum product is 625}} \)