Question

The ratio of two number is 7:3 and their sum is 50 what are the two numbers

Answer 1

The two numbers are 35 and 15

Given :

Two numbers are in the ratio 7 : 3 and their sum is 50

To find :

The two numbers

Solution :

Step 1 of 2 :

Form the equation

Here it is given that the two numbers are in the ratio 7 : 3

Let the numbers are 7x and 3x

Now their sum is 50

By the given condition 7x + 3x = 50

Step 2 of 2 :

Find the numbers

$\displaystyle \sf{ 7x + 3x = 50 }$

$\displaystyle \sf{ \implies 10x = 50}$

$\displaystyle \sf{ \implies x = \frac{50}{10} }$

$\displaystyle \sf{ \implies x = 5 }$

First number = 7x = 7 × 5 = 35

Second number = 3x = 3 × 5 = 15

Hence the two numbers are 35 and 15

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Answer 2

The two numbers are 35 and 15.

Concept to be used:

Any ratio of the form a : b can also be written as the fraction $\dfrac{a}{b}$.

Given data:

The ratio of two numbers is 7 : 3 and their sum is 50.

To find:

The two numbers

Step-by-step explanation:

Since the sum of the two numbers is 50, we can take the two numbers to be x and (50 - x), where x > (50 - x).

Given that, the ratio of the two numbers is 7 : 3. Then

x : (50 - x) = 7 : 3

⇒ $\dfrac{x}{50-x}=\dfrac{7}{3}$

⇒ 3 × x = 7 × (50 - x)

⇒ 3x = 350 - 7x

⇒ 3x + 7x = 350

⇒ 10x = 350

⇒ x = $\dfrac{350}{10}$

⇒ x = 35

Then, 50 - x = 50 - 35 = 15

Final answer:

The two numbers are 35 and 15.

Check step:

The two numbers are 35 and 15.

Their ratio = 35 : 15 = 7 : 3, which is given in the question.

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