Step by step
The question
Question: Kim wants to earn $150 interest in 3 years.
The bank pays 2% simple interest per year.
How much must she put in?
1 Find what we know
What do we know?
The interest: $150.
The time: 3 years.
The rate: 2% each year.
What do we want?
The money put in.
2 Name the unknown
We don't know the money put in.
So we call it x.
2% means 2 out of 100: 2/100.
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 × 2/100 × 3 = 150.
Now we solve it.
Careful!
2% is 2 out of 100.
So in the rule it is 2/100, not 2.
4 Multiply the numbers we know
The numbers we know: 2/100, times 3 years.
2 times 3 is 6.
So x times 6/100.
Simplify: 6/100 is 3/50.
x times 3/50 is 3 x/50.
5 Remove the fraction
The bottom number is 50.
Times 50 will remove it.
We multiply every part by 50.
We do it on both sides, so they stay equal.
50 divided by 50 is 1.
Write what is left.
Do the multiplications.
No more fractions!
6 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
7500 divided by 3 is 2500.
So x = 2500!
7 Answer the question
So the money put in is $2500.
8 Check
Let's check in the story.
In 1 year: 2/100 of $2500 is $50.
3 years: $150 of interest, like the story says.
Does it make sense?
The interest is less than the money put in.
That makes sense for 2% 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.