The difference between two numbers is 15. Four times the larger number is nine times the smaller. Find the two numbers.

The numbers are 27 and 12

Step-by-step explanation:

Let the smaller number be x and the larger number be y.

If the difference between them is 15, then

Also , four times the larger number is nine times the smaller.

From equation (1),

We put the 3rd equation into the 2nd to get:

Expand to get:

Group similar terms

Therefore the larger number is