SOLUTION: The difference of two numbers is 35, the difference of their squares is 315. What are these numbers?

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Question 1099464: The difference of two numbers is 35, the difference of their squares is 315. What are these numbers?
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
 = 315  ====>

(x-y)*(x+y) = 315  ====>  replace (x-y) by 35, based on the condition. You will get

35*(x+y) = 315  ====>  x + y =  = 9.


Thus you reduced the given non-linear system to the simple LINEAR one, consisting of two equations

x - y = 35,
x + y =  9.
-------------------Add the two equations. You will get

2x = 35 + 9 = 44  ====>  x =  = 22.


One number is 22.  Then the other is  y = 22 - 35 = -13.


Check.   = 315.  ! Correct !


Answer.  The numbers are  22  and  -13.


Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
The difference of two numbers is 35, the difference of their squares is 315. What are these numbers?
---------
The other tutor's answer is close.
---
Obviously, it's -22 and 13
Or -13 and 22
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