What are the numbers?

Question

The difference between two numbers is 16. Three times the larger number is seven times the smaller. What are the numbers?  

Answer 1

let x = the larger number, and 7 = the smaller number

then x - y = 16

x = 16 + y

 

3x = 7y

substituting for x, we get 3(16 + y) = 7y

48 + 3y = 7y

solving y = 12

so x = 28

 

Proof: 3 x 28 = 7 x 12; 84 = 84