Final answer:
The sum of two numbers is 41 and the difference is 23. By solving the system of equations, we can find the two numbers and calculate their product. The product of the two numbers is 288, or option (d).
Step-by-step explanation:
The sum of two numbers is 41, and the difference is 23. Let's solve this problem using algebra.
Let's call one of the numbers 'x' and the other number 'y'.
We have two equations:
x + y = 41 ---- (equation 1)
x - y = 23 ---- (equation 2)
To solve the system of equations, we can add equation 1 and equation 2:
(x + y) + (x - y) = 41 + 23
2x = 64
x = 32
Now, substitute the value of x into equation 1:
32 + y = 41
y = 41 - 32
y = 9
The two numbers are 32 and 9. To find their product, we multiply them:
32 * 9 = 288
Therefore, the product of the two numbers is 288. So, the correct answer is (d) 288.