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Question
If (x - 9) : (3x + 6) is the duplicate ratio of 4: 9, find the value of x.
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Solution
The duplicate ratio of a: b is a2: b2
It is given that the duplicate ratio of (x - 9):(3x + 6) = 4:9
Thus,
`(x - 9) :(3x + 6) = 4^2 : 9^2`
`=> (x - 9)/(3x + 6) = 4^2/9^2`
`=> (x -9)/(3x + 6) = 16/81`
⇒ 81x - 729 = 48x + 96
⇒ 81x - 48x = 96 + 729
⇒ 33x = 825
`=> x = 825/33`
`=> x = 25`
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