The problem states that four numbers are in the ratio 11:19:5:7. The sum of these four numbers is 2289. We need to find the sum of the first and third numbers.

1. Problem Description

The problem states that four numbers are in the ratio 11:19:5:

7. The sum of these four numbers is

2

2

8

9. We need to find the sum of the first and third numbers.

2. Solution Steps

Let the four numbers be $11x$, $19x$, $5x$, and $7x$.

The sum of these numbers is given as

2

2

8

9. So, we have

$11x + 19x + 5x + 7x = 2289$

$42x = 2289$

$x = \frac{2289}{42} = \frac{763}{14} = 54.5$

The first number is $11x = 11 \times 54.5 = 599.5$.

The third number is $5x = 5 \times 54.5 = 272.5$.

The sum of the first and third numbers is $11x + 5x = 16x$.

Therefore, the required sum is $16x = 16 \times 54.5 = 872$.

3. Final Answer

872