# 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 2.5 ........ ........ 15 Y 5 8 12 ..........

(ii)

 X 5 ........ 10 35 25 ......... Y 8 12 ........ .......... .......... 32

(iii)

 X 6 8 10 ........ 20 Y 15 20 .......... 40 .............

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(i)

 X 2.5 4 6 15 Y 5 8 12 30

$\frac{2.5}{5}$ = $\frac{x_1}{8}$

On cross multiplication, we get

2.5 x 8 = x1 x 5

x1 = $\frac{2.5\times 8}{5}$ = 4

$\frac{4}{8}$ = $\frac{x_2}{12}$

On cross multiplication, we get

4 x 12 = 8 x x2

$\frac{48}{8}$ = x2

6 = x2

$\frac{6}{12}$ = $\frac{15}{x_3}$

On cross multiplication, we get

15 x 12 = 6 x x3

$\frac{180}{6}$ = x3

30 = x3

(ii)

 X 5 7.5 10 35 25 20 Y 8 12 16 56 40 32

$\frac{5}{8}$ = $\frac{x_1}{12}$

On cross multiplication, we get

5 x 12 = x1 x 8

x1 = $\frac{5\times 12}{8}$ = 7.5

$\frac{7.5}{12}$ = $\frac{10}{x_2}$

On cross multiplication, we get

10 x 12 = 7.5 x x2

$\frac{120}{7.5}$ = x2

16 = x2

$\frac{10}{16}$ = $\frac{35}{x_3}$

On cross multiplication, we get

16 x 35 = 10 x x3

$\frac{16\times 35}{10}$ = x3

56 = x3

$\frac{35}{56}$ = $\frac{25}{x_4}$

On cross multiplication, we get

56 x 25 = 35 x x4

40 = x4

$\frac{25}{40}$ = $\frac{x_5}{32}$

On cross multiplication, we get

25 x 32 = 40 x x5

$\frac{25\times 32}{40}$ = x5
20 = x5

(iii)

 X 6 8 10 16 20 Y 15 20 25 40 50

$\frac{8}{20}$$\frac{10}{x_1}$

On cross multiplication, we get

10 x 20 = x1 x 8

x1 = $\frac{10\times 20}{8}$ = 25

$\frac{10}{25}$ = $\frac{x_2}{40}$

On cross multiplication, we get

10 x 40 = 25 x x2

$\frac{400}{25}$ = x2

16 = x2

$\frac{16}{40}$ = $\frac{20}{x_3}$

On cross multiplication, we get

20 x 40 = 16 x x3

$\frac{20\times 40}{16}$ = x3

50 = x3