Question

If x varies directly as y, and x = 27 when y=6, find x when y=2

Answer 1

Easiest way to solve these problems would be setting up a proportion.

$\frac{27}{6} = \frac{x}{2}$

Let x = ... well... our missing x

Now, we crossmultiply.

6x = 27(2)

6x = 54

x = 54/6

x = 9

Answer 2

Variations can be direct, inverse or joint variation.

The value of x when y = 2, is 9.

The variation is given as:

$\mathbf{x\ \alpha\ y}$

Express as an equation

$\mathbf{x= ky}$

x = 27, when y = 6.

So, we have:

$\mathbf{27= 6k}$

Divide both sides by 6

$\mathbf{4.5 = k}$

Rewrite as:

$\mathbf{k = 4.5 }$

When y = 2, we have:

$\mathbf{x= ky}$

Substitute values for k and y

$\mathbf{x = 4.5 \times 2}$

$\mathbf{x = 9}$

Hence, the value of x when y = 2, is 9.

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