One number is 4 more than another. The difference between their squares is 72. What are the numbers?

Question

help I've been stuck on it for 20 minutes 

Answer 1

Let x = larger number and y = smaller number

 

Then, x = y+4  and  x² - y² = 72

 

So, (y+4)² - y² = 72

 

       y² + 8y + 16 - y² = 72

 

                    8y + 16 = 72

 

                             8y = 56

 

                               y = 7  and x = y+4 = 11

 

 

Answer 2

The numbers are 7 and 11.

 

11 squared is 121. 7 squared is 49.

 

121-49 is 72. 11 is also 4 more than 7. Hope this helped