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

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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]
 
 
 

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