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Question
Fill in the blanks of the following.
`a/3 = b/4 = c/7 = (a-2b+3c)/("______") = ("______")/ (6 - 8 +14)`
Solution
⇒ `a/3 = b/4 = c/7 = [a-2b+3c]/bb16 = bb(2a -2b+2c)/{6-8+14}`
Explanation:
`a/3 = b/4 = c/7 = [-2 xx b]/[-2 xx 4] = [3 xx c]/[3 xx 7]`
⇒ `a/3 = b/4 = c/7 = [-2b]/-8 = [3c]/21 ={a +(-2b)+3c}/{3+(-8) + 21}` ...(Theorem of Equal ratios)
⇒ `a/3 = b/4 = c/7 = (a-2b +3c)/16`
Also,
`a/3 = b/4 = c/7 = (2 xx a)/(2 xx 3) = (-2 xx b)/(-2 xx 4) = [2 xx c]/[2 xx 7]`
⇒ `a/3 = b/4 = c/7 = (2a)/6 = (-2b)/-8 = (2c)/14 = [2a+(-2b)+2c]/[6+(-8)+14]`
⇒ `a/3 = b/4 = c/7 = [a-2b+3c]/16 = (2a -2b+2c)/{6-8+14}`
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