Step by step
The question
Question: c varies directly with n.
c = 18 when n = 6.
Find c when n = 11.
1 Write the rule
Varies directly means c is always the same number times n.
When n gets bigger, c gets bigger too.
We call the number k: c = kn.
k stays the same for every pair of numbers.
Books call it the constant of variation.
2 Find k
We put in c = 18 and n = 6.
k times 6 is written 6k.
6k means 6 times k.
We want just k.
To remove times 6, we divide by 6.
We do it on both sides, so they stay equal.
Careful!
k is c divided by n: 18/6.
Not 6/18.
The c number goes on top.
18/6 on the left.
6k/6 on the right.
6 divided by 6 is 1.
So just k is left.
18 divided by 6 is 3.
So k = 3.
3 Write the equation
We put 3 in place of k.
So the equation is c = 3n.
4 Find c
We put in n = 11.
3 times 11 is 33.
So c = 33.
5 Check
Let's check.
In direct variation, c divided by n is always k.
First pair: 18/6 is 3.
New pair: 33/11 is 3 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 c.
Last: check.