y varies inversely as x. y = 8 when x = 3. Find y when x = 5.

Step by step

The question

Question: y varies inversely as x.

y = 8 when x = 3.

Find y when x = 5.

1 Write the rule

Varies inversely means y is a number divided by x.

When x gets bigger, y gets smaller.

We call the number k: y = k over x.

k stays the same for every pair of numbers.

Books call it the constant of variation.

2 Find k

We put in y = 8 and x = 3.

k/3 means k divided by 3.

We want just k.

To remove divided by 3, we multiply by 3.

We do it on both sides, so they stay equal.

Divided by 3, then times 3: they cancel.

Cross them out.

8 times 3 is 24.

So k = 24.

3 Write the equation

We put 24 in place of k.

So the equation is y = 24 over x.

4 Find y

We put in x = 5.

Careful!

Inverse is not direct.

x got bigger, from 3 to 5.

So y must get smaller.

So y = 24/5.

5 Check

Let's check.

In inverse variation, x times y is always k.

First pair: 3 times 8 is 24.

New pair: 5 times 24/5 is 24 too.

The same k.

So the answer is right!

Let's look back.

First: write the rule.

Then: find k.

Then: write the equation.

Then: find y.

Last: check.