Four numbers are in the ratio 11:19:5:7. The sum of these four numbers is 2289. Find the sum of the first and the third numbers.

1. Problem Description

Four numbers are in the ratio 11:19:5:

7. The sum of these four numbers is

2

2

8

9. Find the sum of the first and the third numbers.

2. Solution Steps

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

The sum of the four numbers is given as

2

2

8

9. Therefore,

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

$42x = 2289$

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

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 $11x + 5x = 16x = 16 \times 54.5 = 872$.

Alternatively:

We are given the ratio of the four numbers as 11:19:5:

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

We are given that their sum is

2

2

8

9. Therefore,

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

$42x = 2289$

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

We have $x = \frac{2289}{42}$.

The required sum is $16x = 16 \times \frac{2289}{42} = \frac{16}{42} \times 2289 = \frac{8}{21} \times 2289$.

$16x = \frac{18312}{42} = 436$.

We want to find the sum of the first and the third number, which is $11x + 5x = 16x$. We found earlier that $42x = 2289$, so we have $x = \frac{2289}{42}$.

Therefore $16x = 16 \cdot \frac{2289}{42} = \frac{16}{42} \cdot 2289 = \frac{8}{21} \cdot 2289 = \frac{18312}{21} = 872$.

3. Final Answer

872