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Question
Fill in the blanks of the following.
`x/7 = y/3 = (3x + 5y)/("_____") = (7x -9y)/("_____")`
Solution
`x/7 = y/3 = (3x + 5y)/bb(36) = (7x -9y)/bb(22)`
Explanation:
`x/7 = y/3 = (3 xx x)/(3 xx 7) = (5 xx y)/( 5 xx 3)`
⇒ `x/7 = y/3 = [3x]/21 = [5y]/15 = (3x + 5y)/( 21 + 15)` ...(Theorem of equal ratios)
⇒ `x/7 = y/3 = (3x+5y)/36`
Also,
`x/7 = y/3 = (7 xx x)/( 7 xx 7) = ( -9 xx y)/( -9 xx 3)`
⇒ `x/7 = y/3 = (7x)/( 49) = ( -9y)/( -27) = (7x - 9y)/[49 + (- 27)]` ...(Theorem of equal ratios)
⇒ `x/7 = y/3 = ( 7x - 9y)/22`
`therefore x/7 = y/3 = [3x + 5y]/36 = [ 7x - 9y]/22`
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