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# find two positive numbers whose difference is 16 and whose product is 1232

find two positive numbers whose difference is 16 and whose product is 1232

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.
1. Find two positive numbers whose difference is 16:  y-x = 16
2. 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 + x2 = 1232

x2 + 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]