Complete the following table, given that x varies directly as y.

x 4 9 … … 3 …

y 16 … 48 36 … 4

x 4 9 ... ... 3 ...

y 16 ... 48 36 ... 4

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Solution

We know k = x/y

4/16 = 9/y₁

By cross-multiplying

4y₁ = 9(16)

= 144

y₁ = 144/4

= 36
( 0.5 marks )

We know k = x/y

9/36 = x₁/48

By cross-multiplying

9(48) = 36x₁

432 = 36x₁

x₁ = 432/36

= 12
( 0.5 marks )

We know k = x/y

12/48 = x₂/36

By cross-multiplying

12(36) = 48x₂

432 = 48x₂

x₂ = 432/48

= 9
( 0.5 marks )

We know k = x/y

9/36 = 3/y₂

By cross-multiplying

9y₂ = 3(36)

= 108

y₂ = 108/9

= 12
( 0.5 marks )

We know k = x/y

3/12 = x₃/4

By cross-multiplying

3(4) = 12x₃

12 = 12x₃

x₃ = 12/12

= 1
( 0.5 marks )

x 4 9 12 9 3 1

y 16 36 48 36 12 4

( 0.5 marks )

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