Question

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 ________.

Answer 1

Answer:   x = 6

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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

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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.

Answer 2

Answer:

Given

• ↦ Three numbers are in the ratio 2 : 3 : 4
• ↦ The sum of number is 54.
• ↦ 'x' is the common factor

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To Find

• ↦ Value of 'x'

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Solution

Let the numbers,

• ↦ 2x
• ↦ 3x
• ↦ 4x

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According to the question,

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

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

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

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

$: \implies\sf{x = 6}$

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

Hence, The value of x is 6.

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Thus numbers are,

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

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Verification

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

• Substituting the numbers

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

$: \implies\sf{54= 54}$

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

Hence Proved!!