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

12 and 28

Step-by-step explanation:

Represent the numbers using x and y. Then y - x = 16. (y is the larger one.)

Then 3y = 7x, and y = (7/3) x.

Substituting (7/3) x for y in y - x = 16, we get:

(7/3) x - x = 16.

Eliminate the fraction by multiplying all three terms by 3:

7x - 3x = 48, or 4x = 48, yielding x = 12. Then y = (7/3) (12) = 28.