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 the third number.

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 the third number.

2. Solution Steps

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

Their sum is given as

2

2

8

9. Therefore,

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

$42x = 2289$

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

We need to find the sum of the first and third numbers, which is $11x + 5x = 16x$.

$16x = 16 \times \frac{2289}{42} = 16 \times \frac{763}{14} = 8 \times \frac{763}{7} = \frac{6104}{7} = 872$

3. Final Answer

The sum of the first and third numbers is 872.