Step by step
The question
Question: Leo puts $600 in a bank at 5% simple interest per year.
He earns $90 interest.
How many years does it take?
1 Find what we know
What do we know?
The money put in: $600.
The rate: 5% each year.
The interest: $90.
What do we want?
The number of years.
2 Name the unknown
We don't know the number of years.
So we call it x.
5% means 5 out of 100: 5/100.
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 600 × 5/100 × x = 90.
Now we solve it.
Careful!
5% is 5 out of 100.
So in the rule it is 5/100, not 5.
4 Multiply the numbers we know
Cancel first.
600 and 100 can both be divided by 100.
600 becomes 6, and the 100 is gone.
Write what is left.
Multiply the numbers: 6 times 5 is 30.
So it is 30x.
5 Remove the 30
30x means 30 times x.
We want just x.
To remove times 30, we divide by 30.
We do it on both sides, so they stay equal.
30 divided by 30 is 1.
So just x is left.
90 divided by 30 is 3.
So x = 3!
6 Answer the question
So it takes 3 years.
7 Check
Let's check in the story.
In 1 year: 5/100 of $600 is $30.
3 years: $90 of interest, like the story says.
Does it make sense?
The interest is less than the money put in.
That makes sense for 5% 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.