Step by step
The question
Question: P = 8n + 5 is the price, in dollars, of a pizza with n toppings.
What does 8 mean?
We write the equation big, so we can label it.
1 What the letters mean
P is the price of a pizza, in dollars.
n is the number of toppings.
2 Make a small table
To see what each number does, we try a few toppings: 0, 1 and 2.
0 is where it starts.
n = 0: 8 times 0 is 0.
Plus 5 is 5.
n = 1: 8 times 1 is 8.
Plus 5 is 13.
n = 2: 8 times 2 is 16.
Plus 5 is 21.
Look at the values of P: 5, 13, 21.
Each time n goes up 1, P goes up by 8.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
And 5?
At n = 0, 8 times 0 is 0.
Only 5 is left: the first number in the table.
So 5 is the price of a pizza at 0 toppings: the start.
Where does plus 8 each time come from?
From 8n: 8 times n.
Each extra topping adds one more 8.
Careful!
8 is multiplied by n, so each topping adds another 8.
The start is the number alone.
4 Say it in words
So 8 means: the price of a pizza goes up 8 dollars for each extra topping.
5 Check
Let's check with n = 3.
In words: start at 5, then add 8 three times.
We get 29.
The equation with n = 3: 8 times 3 is 24.
Plus 5 gives 29 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.