Question

sum of the two numbers is 42 four times the smaller number is equal to 3 times the larger number find the numbers

Answer 1

STEP 1: Define x:

Let the smaller number be x

The bigger number is 42 - x

.

STEP 2: Form the equation:

4 times the smaller number is equal to 3 times the larger number:

4x = 3(42 - x)

.

STEP 3: Solve x:

4x = 3(42 - x)

4x = 126 - 3x

7x = 126

x = 18

.

STEP 4: Find the two numbers:

smaller number = x = 18

larger numer = 42 - x = 42 - 18 = 24

.

Answer: The numbers are 18 and 24

Answer 2

$\textbf{Solution:}$

Given data: sum of the two numbers is 42 four times the smaller number is equal to 3 times the larger number .

So,

Let the smaller number be x and the larger number is y.

given-

4x = 3y ...........(1)

and,

x + y = 42 ........(2)

Now,

=> 4x = 3y

=> x = 3y/4

Substituting the value of x in equation (2)

=> x + y = 42

$= > \frac{3y}{4} + y = 42 \\ \\ = > \frac{3y + 3y}{4} = 42 \\ \\ = > \frac{6y}{4} = 42 \\ \\ = > 7y = 42 \times 4 \\ \\ = > y = \frac{42 \times 4}{7} = 24$

Now,

On substituting the value of y in

x + y = 42

=> x + 24 = 42

=> x = 42 - 24

=> x = 18

Therefore, the required numbers are

$\textbf{x = 18 and y = 24}$

___________________

ᴛʜᴀɴᴋ ʏᴏᴜ ☺️☺️