Question

The sum of three consecutive multiples of 9 is 297. Find the numbers.

Answer 1

Given :-  

• The sum of three consecutive multiples of 9 is 297.  

To Find :-  

• Find the numbers.

Solution :-  

~Here, we’re given that sum of three consecutive multiples of 9 is 297. We can find out the multiples by making an equation satisfying the given condition and then solve it.  

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Let the multiples be  

• x  
• x + 9  
• x + 18  

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ATQ ::  

$\sf \implies ( x ) + ( x + 9 ) + ( x + 18 ) = 297$

$\sf \implies x + x + 9 + x + 18 = 297$

$\sf \implies 3x + 27 = 297$

$\sf \implies 3x = 297 - 27$

$\sf \implies 3x = 270$

$\sf \implies x = \dfrac{270}{3}$

$\sf \implies x = 90$

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Therefore ,  

• Multiples are 90 , 99 , 108  

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Verification :-  

~We’re given that their sum is 297 . Then sum of 90 , 99 and 108 must be 297.  

$\sf \implies 90 + 99 + 108 = 297$

$\sf \implies 297 = 297$

LHS = RHS  

Hence , the answer is correct  ☑

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Answer 2

Given :-

• The sum of three consecutive multiples of 9 is 297.

To Find :-

• Numbers

Solution :-

❏ As we know that, Multiples of 9 are 9 , 18 , 27, 36 and so on. Therefore :

⟼ Let the First Number be x

⟼ Let the Second Number be x + 9

⟼ Let the Third Number be x + 18

According to the Question :

➞ x + x + 9 + x + 18 = 297

➞ x + x + x + 9 + 18 = 297

➞ 3x + 27 = 297

➞ 3x = 297 - 27

➞ 3x = 270

➞ x = 270 / 3

➞ x = 90

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Therefore :

• First Number = x = 90
• Second Number = x + 9 = 90 + 9 = 99
• Third Number = x + 18 = 90 + 18 = 108

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