Step by step
The question
Question: Lina puts $900 in a bank at 4% simple interest per year.
She earns $108 interest.
How many years does it take?
1 Find what we know
What do we know?
The money put in: $900.
The rate: 4% each year.
The interest: $108.
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.
4% means 4 out of 100: 4/100.
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 900 × 4/100 × x = 108.
Now we solve it.
Careful!
4% is 4 out of 100.
So in the rule it is 4/100, not 4.
4 Multiply the numbers we know
Cancel first.
900 and 100 can both be divided by 100.
900 becomes 9, and the 100 is gone.
Write what is left.
Multiply the numbers: 9 times 4 is 36.
So it is 36x.
5 Remove the 36
36x means 36 times x.
We want just x.
To remove times 36, we divide by 36.
We do it on both sides, so they stay equal.
36 divided by 36 is 1.
So just x is left.
108 divided by 36 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: 4/100 of $900 is $36.
3 years: $108 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.