Step by step
The question
Question: S = 50m + 200 is the money in a savings account, in dollars, after m months.
What does 50 mean?
We write the equation big, so we can label it.
1 What the letters mean
S is the money, in dollars.
m is the number of months.
2 Make a small table
To see what each number does, we try a few months: 0, 1 and 2.
0 is where it starts.
m = 0: 50 times 0 is 0.
Plus 200 is 200.
m = 1: 50 times 1 is 50.
Plus 200 is 250.
m = 2: 50 times 2 is 100.
Plus 200 is 300.
Look at the values of S: 200, 250, 300.
Each time m goes up 1, S goes up by 50.
The same number every time.
3 Find the numbers in the table
Now we write the equation again, and label its numbers.
And 200?
At m = 0, 50 times 0 is 0.
Only 200 is left: the first number in the table.
So 200 is the money at 0 months: the start.
Where does plus 50 each time come from?
From 50m: 50 times m.
Each extra month adds one more 50.
Careful!
50 is multiplied by m, so each month adds another 50.
The start is the number alone.
4 Say it in words
So 50 means: the money goes up 50 dollars for each extra month.
5 Check
Let's check with m = 3.
In words: start at 200, then add 50 three times.
We get 350.
The equation with m = 3: 50 times 3 is 150.
Plus 200 gives 350 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.