Question

The sum of three numbers is 350. If the ratio of the first to the second is 23, and that of the second to
the third is 45, then what is the second number?​

Answer 1

Answer:

sum of three numbers=350

let first number= x

then, second number = y

third number = 45

Step-by-step explanation:

first : second = x : y

x : y = 23

x /y = 23

x = 23 y

23y + y + 45 = 350

24y + 45- 350 = 0

24y - 305 = 0

24y = 305

y= 305/24

y = 12.70

Answer 2

Given:

Sum of three numbers = 350

Ratio of first to second = 2:3

Ratio of second to third = 4:5

To find:

The value of second number.

Solution:

Let the three numbers be $x,y,z$

According to the given information,

$x:y=2:3...(1)$

$\frac{x}{y} =\frac{2}{3}$

$y:z=4:5...(2)$

$\frac{y}{z}=\frac{4}{5}$

In order to get the ratio between all three numbers as $x:y:z$, we need to make the ratios of the second number equal in both equations (1) and (2).

On multiplying equation (1) with $4$ and equation (2) with $3$, we get,

$x:y=8:12...(3)$

$y:z=12:15...(4)$

From equations (3) and (4), we can see that $12$ is common in both for $y$. Thus, we club $12$ when we combine the ratios as shown below.

Hence, we can write the ratio as,

$x:y:z=8:12:15$

Add the ratios

$x+y+z=8+12+15=35$

To determine the second number, divide the number in the middle of the ratio $(12)$ by the sum of ratio $(35)$ and multiply the result with the sum of three numbers $(350)$.

$y=\frac{12}{35}*350=120$

Thus, the second number is $120$.

The second number is 120 from a set of three numbers whose sum is 350.