Step by step
The question
Question: Ana puts $800 in a bank for 2 years.
She earns $64 interest.
What is the interest rate per year?
1 Find what we know
What do we know?
The money put in: $800.
The time: 2 years.
The interest: $64.
What do we want?
The rate.
2 Name the unknown
We don't know the rate.
So we call it x.
x percent means x out of 100: x/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 800 × x/100 × 2 = 64.
Now we solve it.
Careful!
The rate is x percent.
So in the rule it is x/100, not just x.
4 Multiply the numbers we know
Cancel first.
800 and 100 can both be divided by 100.
800 becomes 8, and the 100 is gone.
Write what is left.
Multiply the numbers: 8 times 2 is 16.
So it is 16x.
5 Remove the 16
16x means 16 times x.
We want just x.
To remove times 16, we divide by 16.
We do it on both sides, so they stay equal.
16 divided by 16 is 1.
So just x is left.
64 divided by 16 is 4.
So x = 4!
6 Answer the question
So the rate is 4% a year.
7 Check
Let's check in the story.
In 1 year: 4/100 of $800 is $32.
2 years: $64 of interest, like the story says.
Does it make sense?
The interest is less than the money put in.
That makes sense for 4% 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.