If (x - 9) : (3x + 6) is the duplicate ratio of 4 : 9, find the value of x.
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Duplicate ratio of 4 : 9 = 42 : 92 = 16 : 81.
According to question,
(x - 9) : (3x + 6) = 16 : 81
⇒x−93x+6=1681⇒81(x−9)=16(3x+6)⇒81x−729=48x+96⇒81x−48x=96+729⇒33x=825⇒x=82533x=25.\Rightarrow \dfrac{x - 9}{3x + 6} = \dfrac{16}{81} \\[0.5em] \Rightarrow 81(x - 9) = 16(3x + 6) \\[0.5em] \Rightarrow 81x - 729 = 48x + 96 \\[0.5em] \Rightarrow 81x - 48x = 96 + 729 \\[0.5em] \Rightarrow 33x = 825 \\[0.5em] \Rightarrow x = \dfrac{825}{33} \\[0.5em] x = 25.⇒3x+6x−9=8116⇒81(x−9)=16(3x+6)⇒81x−729=48x+96⇒81x−48x=96+729⇒33x=825⇒x=33825x=25.
Hence, the value of x is 25.
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