Question

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	.............

 

Answer 1

(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