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WARRIOR [948]
2 years ago
12

Three numbers are in the ratio 2 : 3 : 4 and their sum is 54. If 'x' is the common factor, then the value of 'x' is ________.

Mathematics
2 answers:
Sloan [31]2 years ago
8 0
<h3>Answer:   x = 6</h3>

========================================================

Explanation:

The ratio 2:3:4 scales up to 2x:3x:4x after multiplying all three parts by x.

Their sum is 54, so we can say 2x+3x+4x = 54

Solve for x

2x+3x+4x = 54

9x = 54

x = 54/9

x = 6

------------------

Extra info:

if x = 6, then,

  • 2x = 2*6 = 12
  • 3x = 3*6 = 18
  • 4x = 4*6 = 24

Then notice how 2x+3x+4x = 12+18+24 = 54 to help confirm the answer

Also note how 12:18:24 reduces to 2:3:4 after dividing all three parts by the GCF 6.

Neporo4naja [7]2 years ago
3 0

Answer:

<h3><u>Given</u> </h3>
  • ↦ Three numbers are in the ratio 2 : 3 : 4
  • ↦ The sum of number is 54.
  • ↦ 'x' is the common factor

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

<h3><u>To</u><u> Find</u> </h3>
  • ↦ Value of 'x'

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

<h3><u>Solution</u> </h3>

Let the numbers,

  • ↦ 2x
  • ↦ 3x
  • ↦ 4x

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

According to the question,

: \implies\sf{2x + 3x + 4x = 54}

: \implies\sf{9x = 54}

: \implies\sf{x =  \dfrac{54}{9} }

: \implies\sf {x =  \cancel\dfrac{54}{9}}

: \implies\sf{x = 6}

{\dag{\underline{\boxed{\sf{\purple{x = 6}}}}}}

<u>Hence, The value of x is 6.</u>

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Thus numbers are,

  • ↦ 2 × 6 = 12
  • ↦ 3 × 6 = 18
  • ↦ 4 × 6 = 24

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

<h3><u>Verification</u> </h3>

: \implies\sf{2x + 3x + 4x = 54}

  • Substituting the numbers

: \implies\sf{ 12+ 18 + 24 = 54}

: \implies\sf{54= 54}

{\dag{\underline{\boxed{\sf{\purple{LHS=RHS }}}}}}

Hence Proved!!

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