Question

Two numbers are in the ratio 3:4 and their sum is 84. Find the numbers?

Answer 1

The two numbers are 36 and 48

Given :

Two numbers are in the ratio 3 : 4 and their sum is 84

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 3 : 4

Let the numbers are 3x and 4x

Now their sum is 84

By the given condition

3x + 4x = 84

Step 2 of 2 :

Find the numbers

$\displaystyle \sf{ 3x + 4x = 84 }$

$\displaystyle \sf{ \implies 7x = 84}$

$\displaystyle \sf{ \implies x = \frac{84}{7} }$

$\displaystyle \sf{ \implies x = 12 }$

First number = 3x = 3 × 12 = 36

Second number = 4x = 4 × 12 = 48

Hence the two numbers are 36 and 48

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Answer 2

The two numbers are 36 and 48.

Step by Step Solution.

Given:

The numbers are in ratio of 3:4.

the sum of the number is 84.

Explanation:

Let the first number be X and,

the second number be Y.

So, according to problem,

$\frac{X}{Y} =\frac{3}{4}$

$4X=3Y$

$X=\frac{3Y}{4}$    

Now, the sum of the number is 84.

$X+Y=84$

Put the value of X in above equation,

$\frac{3Y}{4}+Y=84$

Solving above equation for the value of Y,

$Y=48$

Put the value of Y in linear equation and obtain X.

$X=36$

Hence, the obtained numbers are 36 and 48.

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