y is inversely proportional to x. y = 5 when x = 12. Find y when x =… Step by Step

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The question

Question: y is inversely proportional to x.

y = 5 when x = 12.

Find y when x = 10.

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.

y = kx

k stays the same for every pair of numbers.

Books call it the constant of variation.

k stays the same

2 Find k

We put in y = 5 and x = 12.

5 = k12

k/12 means k divided by 12.

We want just k.

To remove divided by 12, we multiply by 12.

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

5 × 12 = k12 × 12

Divided by 12, then times 12: they cancel.

Cross them out.

5 times 12 is 60.

5 × 12 = 60

So k = 60.

k = 60

3 Write the equation

We put 60 in place of k.

So the equation is y = 60 over x.

y = 60x

4 Find y

We put in x = 10.

y = 6010

Careful!

Inverse is not direct.

x got smaller, from 12 to 10.

So y must get bigger.

Careful: not y = 512 × 10 ✗

60 divided by 10 is 6.

So y = 6.

y = 6

5 Check

Let's check.

In inverse variation, x times y is always k.

First pair: 12 times 5 is 60.

x × y: 12 × 5 = 60

New pair: 10 times 6 is 60 too.

The same k.

So the answer is right!

10 × 6 = 60

Let's look back.

First: write the rule.

Then: find k.

Then: write the equation.

Then: find y.

Last: check.

Answer