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 ________.
2 answers:
<h3>
Answer: x = 6</h3>
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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:
<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>
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
<h3><u>Solution</u> </h3>
Let the numbers,
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
According to the question,
![: \implies\sf{2x + 3x + 4x = 54}](https://tex.z-dn.net/?f=%20%3A%20%5Cimplies%5Csf%7B2x%20%2B%203x%20%2B%204x%20%3D%2054%7D)
![: \implies\sf{9x = 54}](https://tex.z-dn.net/?f=%20%3A%20%5Cimplies%5Csf%7B9x%20%3D%2054%7D)
![: \implies\sf{x = \dfrac{54}{9} }](https://tex.z-dn.net/?f=%20%3A%20%5Cimplies%5Csf%7Bx%20%3D%20%20%5Cdfrac%7B54%7D%7B9%7D%20%7D)
![: \implies\sf {x = \cancel\dfrac{54}{9}}](https://tex.z-dn.net/?f=%20%3A%20%5Cimplies%5Csf%20%7Bx%20%3D%20%20%5Ccancel%5Cdfrac%7B54%7D%7B9%7D%7D)
![: \implies\sf{x = 6}](https://tex.z-dn.net/?f=%20%3A%20%5Cimplies%5Csf%7Bx%20%3D%206%7D)
![{\dag{\underline{\boxed{\sf{\purple{x = 6}}}}}}](https://tex.z-dn.net/?f=%7B%5Cdag%7B%5Cunderline%7B%5Cboxed%7B%5Csf%7B%5Cpurple%7Bx%20%3D%206%7D%7D%7D%7D%7D%7D)
<u>Hence, The value of x is 6.</u>
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Thus numbers are,
- ↦ 2 × 6 = 12
- ↦ 3 × 6 = 18
- ↦ 4 × 6 = 24
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
<h3><u>Verification</u> </h3>
![: \implies\sf{2x + 3x + 4x = 54}](https://tex.z-dn.net/?f=%20%3A%20%5Cimplies%5Csf%7B2x%20%2B%203x%20%2B%204x%20%3D%2054%7D)
![: \implies\sf{ 12+ 18 + 24 = 54}](https://tex.z-dn.net/?f=%20%3A%20%5Cimplies%5Csf%7B%2012%2B%2018%20%2B%2024%20%3D%2054%7D)
![: \implies\sf{54= 54}](https://tex.z-dn.net/?f=%20%3A%20%5Cimplies%5Csf%7B54%3D%2054%7D)
![{\dag{\underline{\boxed{\sf{\purple{LHS=RHS }}}}}}](https://tex.z-dn.net/?f=%7B%5Cdag%7B%5Cunderline%7B%5Cboxed%7B%5Csf%7B%5Cpurple%7BLHS%3DRHS%20%7D%7D%7D%7D%7D%7D)
Hence Proved!!
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