Step by step
The question
Question: N = 15 + 4w is the number of books on a shelf after w weeks.
What does 15 mean?
We write the equation big, so we can label it.
1 What the letters mean
N is the number of books.
w is the number of weeks.
2 Make a small table
To see what each number does, we try a few weeks: 0, 1 and 2.
0 is where it starts.
w = 0: 4 times 0 is 0.
15 plus 0 is 15.
w = 1: 4 times 1 is 4.
15 plus 4 is 19.
w = 2: 4 times 2 is 8.
15 plus 8 is 23.
Look at the values of N: 15, 19, 23.
Each time w goes up 1, N goes up by 4.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
Where does plus 4 each time come from?
From 4w: 4 times w.
Each extra week adds one more 4.
And 15?
At w = 0, 4 times 0 is 0.
Only 15 is left: the first number in the table.
So 15 is the number of books at 0 weeks: the start.
Careful!
15 is not multiplied by w.
It is there once, even at 0 weeks.
4 Say it in words
So 15 means: the number of books is 15 at 0 weeks.
That is the start.
5 Check
Let's check with w = 3.
In words: start at 15, then add 4 three times.
We get 27.
The equation with w = 3: 4 times 3 is 12.
15 plus 12 gives 27 too.
So the meaning is right!
Let's look back.
First: what the letters mean.
Then: make a small table.
Then: find the numbers in the table.
Then: say it in words.
Last: check.