Step by step
The question
Question: M = 40 + 15w is the money saved, in dollars, after w weeks.
What does 15 mean?
We write the equation big, so we can label it.
1 What the letters mean
M is the money saved, in dollars.
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: 15 times 0 is 0.
40 plus 0 is 40.
w = 1: 15 times 1 is 15.
40 plus 15 is 55.
w = 2: 15 times 2 is 30.
40 plus 30 is 70.
Look at the values of M: 40, 55, 70.
Each time w goes up 1, M goes up by 15.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
And 40?
At w = 0, 15 times 0 is 0.
Only 40 is left: the first number in the table.
So 40 is the money saved at 0 weeks: the start.
Where does plus 15 each time come from?
From 15w: 15 times w.
Each extra week adds one more 15.
Careful!
15 is multiplied by w, so each week adds another 15.
The start is the number alone.
4 Say it in words
So 15 means: the money saved goes up 15 dollars for each extra week.
5 Check
Let's check with w = 3.
In words: start at 40, then add 15 three times.
We get 85.
The equation with w = 3: 15 times 3 is 45.
40 plus 45 gives 85 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.