Question

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

Answer 1

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

$y - x = 15....(1)$

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

$4y = 9x.....(2)$

From equation (1),

$y = x + 15....(3)$

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

$4(x + 15) = 9x$

Expand to get:

$4x + 60 = 9x$

Group similar terms

$9x - 4x = 60$

$5x = 60$

$x = 12$

Therefore the larger number is

$y = 12 + 15 = 27$