Step by step
The question
Question: Zoe puts $450 in a bank at 3% simple interest per year.
How much interest does she earn in 1 year?
1 Find what we know
What do we know?
The money put in: $450.
The rate: 3% each year.
The time: 1 year.
What do we want?
The interest.
2 Name the unknown
We don't know the interest.
So we call it x.
3% means 3 out of 100: 3/100.
Here is the rule for it.
Interest = money put in, times the rate, times the years.
In short: I = P × r × t.
Interest is extra money for using money.
Simple interest is the same amount every year.
3 Write the equation
In words: the money put in, times the rate, times the years, makes the interest.
So the equation is x = 450 × 3/100 × 1.
Now we solve it.
Careful!
3% is not 3.
It means 3 out of 100: 3/100.
Without the 100, the interest would be $1350: more than the money put in!
4 Multiply the numbers we know
Cancel first.
450 and 100 can both be divided by 50.
450 becomes 9, and 100 becomes 2.
Write what is left.
Multiply the whole numbers: 27.
So x is 27/2.
27 divided by 2 is 13.5.
Now we have x = 13.5.
5 Remove the decimals
Decimals are hard to work with.
Let's get rid of them.
We multiply every part by 10.
We do it on both sides, so they stay equal.
Times 10 moves the point 1 place to the right.
10 × x = 10x.
10 × 13.5 = 135.
Write the answers.
No more decimals!
6 Remove the 10
10x means 10 times x.
We want just x.
To remove times 10, we divide by 10.
We do it on both sides, so they stay equal.
10 divided by 10 is 1.
So just x is left.
135 divided by 10 is 13.5.
So x = 13.5!
7 Answer the question
27/2 is 13.5.
So the interest is $13.50.
8 Check
Let's check in the story.
In 1 year: 3/100 of $450 is $13.50.
1 year: $13.50 of interest, like the story says.
Does it make sense?
The interest is less than the money put in.
That makes sense for 3% a year.
So the answer is right!
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the equation.
Then: solve it.
Then: answer the question.
Last: check.