Q.14 The sum of three consecutive multiples of 9 is 324. Find these multiples.


{please explain also}​

2 thoughts on “<br />Q.14 The sum of three consecutive multiples of 9 is 324. Find these multiples.<br /><br /><br />{please explain also}​”

1. Question:-

   • The sum of three consecutive multiples of 9 is 324. Find these multiples.

   To find:-

   • The three consecutive multiples of 9

   Solution:-

   • Let the consecutive multiples be x , x+1 and x+2

   • We are given that the sum of multiples is 324

   • As they are the multiples of 9 the equation formed will be:–

   [tex] \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red \leadsto \: { {\boxed{ \bf \: 9 \times x + 9(x + 1) + 9(x + 2) = 324}}}[/tex]

   [tex] \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \pink \leadsto \bf \: \: 9x + 9x + 9 + 9x + 18 = 324[/tex]

   [tex] \\ \: \: \: \: \: \: \: \: \: \orange \leadsto \bf \: \: 27x + 27 = 324[/tex]

   [tex] \\ \: \: \: \: \: \: \: \: \green \leadsto \bf \: 27x = 324 -27[/tex]

   [tex] \\ \: \: \: \: \: \: \: \: \blue \leadsto \bf \: 27x = 297[/tex]

   [tex] \\ \: \: \: \: \: \: \: \: {\color{navy}{ \leadsto }} \: \bf \: 27x = 297[/tex]

   [tex] \\ \: \: \: \: \: \: \: \: { \color{brown}{\leadsto}} \: \bf \: x = \frac{297}{27} [/tex]

   [tex]\\ \: \: \: \: \: \: \: \: { \color{yellow}{\leadsto}} \: \bf \: x = 11[/tex]

   • Therefore the required value for x is 11.

   Now the multiples would be

   • 11
   • x+1= 11+1=12
   • x+2 =11+2=13

   The multiples are 11,12,13

   ━━━━━━━━━━━━━━━━━━━━━━━━

   [tex]{ \huge{ \underline{ \underline{ \boxed{ \mathfrak{ \color{goldenrod}{Verification : – }}}}}}}[/tex]

   [tex] \\ \: \: \: \: \: \: \: \: \mapsto \: (9 \times 11) +( 9 \times 12) + (9 + 13)[/tex]

   [tex] \\ \: \: \: \: \: \: \: \: \: \: \: \mapsto \: 99 + 108 + 117[/tex]

   [tex] \\ \: \: \: \: \: \: \: \: \: \mapsto \: 324[/tex]

   [tex] \large{ \boxed{ \mathfrak{ \pink{Hence \: verified }}}}[/tex]

   [tex] \color{goldenrod}{━━━━━━━━━━━━━━━━━━━━━━━━━━━━━}[/tex]

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2. Answer:

   thank u for points

   thank u again

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