The sum of two numbers is 83. The difference of the 2 numbers is 13. What is the product of the two numbers? A. 1632 B. 1650 C. 1666 D. 1680

Let's solve this step by step:

Step 1: Let's denote the two numbers as x and y. According to the problem, we have two equations:

x + y = 83 (equation 1, from "The sum of two numbers is 83")

x - y = 13 (equation 2, from "The difference of the 2 numbers is 13")

Step 2: We can solve these two equations simultaneously. Let's add equation 1 and equation 2:

(x + y) + (x - y) = 83 + 13

This simplifies to:

2x = 96

Then, divide both sides by 2 to solve for x:

x = 96 / 2 = 48

Step 3: Now that we have the value for x, we can substitute it into equation 1 to solve for y:

48 + y = 83

Subtract 48 from both sides:

y = 83 - 48 = 35

Step 4: Now that we have both numbers (x = 48, y = 35), we can find their product:

x * y = 48 * 35 = 1680

So, the product of the two numbers is 1680, which corresponds to option D.