difference in squares

Question

One number is 3 more than another. The difference between their squares is 33. What are the numbers?

Answer 1

Let your numbers be x and x+3

 

The difference of their squares is 33 so:

 

(x+3)² - x² = 33

x² + 6x + 9 - x² = 33

6x + 9 = 33

6x = 24

x = 4

x+3=7

 

Your numbers are 4 and 7

 

Check:  7² - 4² = 49 - 16 = 33