Maharashtra State BoardSSC (English Medium) 9th Standard
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Fill in the Blanks of the Following - Algebra

Sum

Fill in the blanks of the following
`x/7 = y/3 = (3x + 5y)/(..........) = (7x -9y)/(.........)`

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Solution

`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`

Concept: Theorem on Equal Ratios
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APPEARS IN

Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 4 Ratio and Proportion
Practice Set 4.4 | Q 1.1 | Page 73
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