Question

The sum of three consecutive multiply of 9 is 999 .find the multiply

Answer 1

GIVEN :-

• Sum of three consecutive multiples of 9 = 999

TO FIND :-

• The three consecutive multiples.

SOLUTION :-

Let,

First multiple = x

Second multiple = x + 9

Third multiple = x + 18

According to the question,

$\longrightarrow \sf x + (x+9) +(x+18) = 999 \\\\\longrightarrow 3x+27 = 999 \\\\\longrightarrow 3x= 999-27 \\\\\longrightarrow 3x = 972 \\\\\longrightarrow x = \dfrac{972}{3} \\\\\longrightarrow\bf x = 324$

First multiple = 324

Second multiple = 324 + 9 = 333

Third multiple = 324 + 18 = 342

The three consecutive multiples of 9 are 324, 333 and 342.

Answer 2

♡ Correct Question:

• The sum of three consecutive multiples of 9 is 999. Mind the multiples.

♡ Answer:

• The numbers are 324 , 333 and 342.

♡ Given:

• The sum of three consecutive multiples of 9 is 999.

♡ To find:

• The three consecutive multiples of 9

♡ Solution:

Let the unknown number be x.

Thus,

$\hookrightarrow$ The first number = 9x

$\hookrightarrow$ The second number = 9x + 9

[Since it is a multiple of 9]

$\hookrightarrow$ The third number = 9x + 18

[Since it is a multiple of 9]

A/q 9x + 9x + 9 + 9x + 18 = 999

$\implies$ 9x + 9x + 9x = 18 + 9 = 999

$\implies$ 27x + 27 = 999

$\implies$ 27x = 999 - 27

$\implies$27x = 972

$\implies$x = $\sf\dfrac{972}{27}$

$\implies$$\boxed{x\: =\: 36}$

$\therefore$ The numbers are :

$\hookrightarrow$ 9 × 36

= 324

$\hookrightarrow$ 9 × 36 + 9

= 324 + 9

= 333

$\hookrightarrow$ 9 × 36 + 18

= 324 + 18

= 342

Hence the numbers are 324 , 333 and 342.

♡ Verification:

$\because$ 9x + 9x + 9 + 9x + 18 = 999

$\implies$ (9x) + (9x + 9) + (9x + 18) = 999

$\implies$ 324 + 333 + 342 = 999

[Substitution of values]

$\implies$ LHS = RHS

Hence verified too!

♡ Concepts Used:

• Assumption of unknown numbers
• Equating the equations
• Substitution of values
• Transposition Method

♡ Extra - Information:

• A linear equation is an equation that may be put in the form where are the variables, and are the coefficients, which are often real numbers.
• The standard form of a linear equation in one variable is represented as ax + b = 0 where, a ≠ 0 and x is the variable.
• Both sides of the equation are supposed to be balanced for solving a linear equation. Equality sign denotes that the expressions on either side of the ‘equal to’ sign are equal.
• Since the equation is balanced, for solving it certain mathematical operations are performed on both sides of the equation in a manner that it does not affect the balance of the equation.