Question

If a sum of two numbers is 21 and the second number is six times the first number what are the numbers

Answer 1

Question:

If the sum of two numbers is 21 and the second number is six times the first number. What are the numbers ?

Answer:

3 , 18

Solution:

Let the two numbers be x (1st number) and

y (2nd number) .

Now,

According to the question,

The sum of two numbers is 21.

Thus,

=> x + y = 21

=> y = 21 - x --------(1)

Also,

The second number is six times the first number.

Thus,

=> y = 6x --------(2)

Now,

From eq-(1) and eq-(2) , we have ;

=> 21 - x = 6x

=> 21 = 6x + x

=> 21 = 7x

=> x = 21/7

=> x = 3

Now,

Putting x = 3 in eq-(2) , we get ;

=> y = 6x

=> y = 6•3

=> y = 18

Thus,

1st number = x = 3

2nd number = y = 18

Hence,

The required numbers are 3 and 18 .

Answer 2

Answer:

Given Information:-

1. Sum of two numbers = 21
2. Second number is 6 times the first number.

To Find:-

The value of the numbers.

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Let the first number be = $\tt{x}$

(Note: It can be of any alphabet)

Second number is therefore = $\tt{6x}$

(Why So? We've written 6x because it is mentioned 6 times. Therefore it is multiplied with it)

ACCORDING TO THE QUESTION:-

$\tt{6x+x=21}$

(Suitable Equation formation to get a suitable value. We have arranged it as it is given first number, i.e. x, and second one, i.e. 6x, yields 21.)

$\tt{\implies 7x = 21}$

(Now, we have added the like terms.)

$\tt{\implies x = \frac {21}{7}}$

(Taken 7 to the Right Hand Side.

Changes: In the LHS, 7 is in the Multiplication form. Value of 7 is then in division form in case of RHS)

$\tt{\implies x = \frac {\cancel {21}}{\cancel {7}}}$

(Cancelled the fraction taking common of the number 7)

$\tt{\implies x = \frac {3}{1}}$

(Divided the nominator and the denominator)

$\boxed{\tt{\implies x = 3 }}$

(Value of x)

____________...

REQUIRED ANSWER:-

$\tt{\therefore}$ Value of:

• 6x = 6×3 = 18

or,

$\boxed{\large\tt{6x=18 \ (Second \ number)}}$

• x = 3

or,

$\boxed{\large\tt{x=3 \ (First \ number)}}$

_______________...

VERIFICATION:-

Equation:-

$\tt{6x+x=21}$

Left Hand Side:-

$\tt{6x+x}$

(As per given in the LHS equation)

$\tt{=18+3}$

(Putting the suitable values. {Available above})

$\tt{=21}$

(Total value is the result)

Right Hand Side:-

$\tt{21}$

$\boxed{\large\tt{\therefore LHS=RHS}}$