*Find two positive numbers whose difference is 16 and whose product is 1232*

Let x = one of the positive numbers

Let y = the other positive number

We have two unknowns, x and y. To find them, we need two equations relating them.

*Find two positive numbers whose difference is 16: * y-x = 16

*Find two positive numbers whose product is 1232: x*y = 1232*

From equation 1:

y-x = 16

So y = 16 + x

Let's substitute 16+x in place of y in equation 2. This will eliminate the y from equation 2 and let us solve for x:

x*y = 1232

x*(16+x) = 1232

16x + x^{2} = 1232

x^{2} + 16x -1232 = 0

(x+44)(x-28) = 0

x = -44, 28

The problem states that the numbers are positive, which eliminates -44.

**x = 28**

**y =** 16 + x = **44**

Check:

y-x = 16

44-28 = 16

16 = 16 [Check]

x*y = 1232

28*44 = 1232

1232 = 1232 [Check]