Complete the following tables given that x varies directly as y.

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Complete the following tables given that x varies directly as y.

(i)

 X 4 9 ......... ........... 3 .......... Y 16 .......... 48 36 ............. 4

(ii)

 X 3 5 7 9 2 ............ 20 28 .............

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(i)

 X 4 9 12 9 3 1 Y 16 36 48 36 12 4

$\frac{4}{16}$ =  $\frac{9}{x_1}$

On cross multiplication, we get

9 x 16 = x1 x 4

x1$\frac{9\times 16}{4}$ = 36

$\frac{9}{36}$ = $\frac{x_2}{48}$

On cross multiplication, we get

9 x 48 = 36 x x2

$\frac{9\times 48}{36}$ = x2

12 = x2

$\frac{12}{48}$ = $\frac{x_3}{36}$

On cross multiplication, we get

12 x 36 = 48 x x3

$\frac{12\times 36}{48}$ = x3

9 = x3

$\frac{9}{36}$ = $\frac{3}{x_4}$

On cross multiplication, we get

36 x 3 = 9 x x4

$\frac{36\times 3}{9}$ = x4

12 = x4

$\frac{3}{12}$ = $\frac{x_5}{4}$

On cross multiplication, we get

3 x 4 = 12 x x5

$\frac{12}{12}$ = x5

1 = x5

(II)

 X 3 5 7 9 2 12 20 28 36

$\frac{5}{20}$ =  $\frac{3}{x_1}$

On cross multiplication, we get

20 x 3 = x1 x 5

x1 $\frac{20\times 3}{5}$ = 12

$\frac{7}{28}$ = $\frac{9}{x_2}$

On cross multiplication, we get

9 x 28 = 7 x x2

$\frac{9\times 28}{7}$ = x2

36 = x2