Answer:
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
[tex]y - x = 15....(1)[/tex]
Also , four times the larger number is nine times the smaller.
[tex]4y = 9x.....(2)[/tex]
From equation (1),
[tex]y = x + 15....(3)[/tex]
We put the 3rd equation into the 2nd to get:
[tex]4(x + 15) = 9x[/tex]
Expand to get:
[tex]4x + 60 = 9x[/tex]
Group similar terms
[tex]9x - 4x = 60[/tex]
[tex]5x = 60[/tex]
[tex]x = 12[/tex]
Therefore the larger number is
[tex]y = 12 + 15 = 27[/tex]
