This lesson presents solution examples of word problems on percentage.
It is a continuation of the lesson Percentage problems in this site.
Let me remind you that 1% of some number is one hundredth (1/100) part of the number.
10% of some number is one tenth (10/100 = 1/10) part of the number.
20% of some number is one fifth (20/100 = 1/5) part of the number.
25% of some number is one fourth (25/100 = 1/4) part of the number.
The percentage problems include three numbers.
One number is the base B . It represents the total amount of something or the measure of something.
Second number is the rate R . It is a measure of the part relatively to the whole thing, expressed in percents, like 3%, 7.5%, 12.75% (percentage).
Third number is the part P . It is the amount or the measure of the part.
The base, the part, and the percentage are connected by the formula .
For example, if the base B is equal to 80 and the percentage R is 25%, then the part P is .
Problems considered in this lesson are all of the same type: you are given two of three numbers, namely the part P and the rate R as percentage.
The third number, the base B , is unknown, and you should find it.
These problems are Type 3 problems on percentage , as defined in the lesson Percentage problems.
Specifically for the Type 3 percentage problems the general formula above can be re-written in the form
. (***)
This formula is the basic to solve the percentage problems of the Type 3.
Below are examples of the Type 3 word problems on percentage.
The student answered correctly 76 questions on the mathematics test, which was 95% of the total number of questions.
How many questions were in the test?
You know that 76 questions are 95% of the total number of questions.
So, you are given the part number ( P ), which is 76, and you are given the rate number ( R ) expressed in percents, which is 95%.
This is the Type 3 percentage problem .
Apply the formula (***).
The total number of questions was
.
Answer . The total number of questions was 80.
Daniel bought a calculator at the store with the tax of 7.5%.
The tax amount was $1.87.
Find the calculator price before tax.
You are given that 7.5% of the calculator price was $1.87.
Thus, you know the part P and the percentage R .
So, this is the the Type 3 percentage problem .
Apply the formula (***) to find the calculator price before tax.
It is equal to
dollars.
Answer . The calculator price before tax was $26.99.
Brian bought a printer on sale at the store. The discount was 15%, and Brian saved $13.50.
What was the printer original price?
You are given the discount amount, it is $13.50. This is the part P of the original price.
You are given that this part is 15% of the original price. This is the rate R , expressed in percents.
So, this is the the Type 3 percentage problem .
Apply the formula (***).
The original price was
dollars.
Answer . The original price for the printer before the discount was $90.00.
The population of Georgetown was 50000 in 2009. The population increased by 3 percents in 2010, or 1500.
What was the population at the end of 2009?
You are given the population increase amount of 1500.
You are given that this amount is 3% of the Georgetown population at the end 2009.
So, you are given the part P and the percentage rate R .
Thus, this is the Type 3 percentage problem .
Apply the formula (***) to calculate the Georgetown population at the end 2009.
You have
.
In other words, 1500/3 = 500 was the measure of 1% of population, or 1/100 part.
Then 100%, the whole population, was 100 times more, or 500 x 100 = 50000.
So, the population of Georgetown was 50000 at the end of 2010.
Answer . The population of Georgetown was 50000 at the end of 2009.
Kathy invested into the bank account for 2% per year.
After one year, Kathy earned $500.00 in this account.
What was Kathy's initial investment?
You are given that $500.00 (the part P ) are 2% (the rate in percents, R ) of the initial sum.
This is the Type 3 percentage problem .
Apply the formula (***) to find the initial investment (the base B ).
The initial investment was
dollars.
In other words, 500.00/2 = 250 was the measure of 1% of Kathy's original investment, or 1/100 part.
Then 100%, the whole original investment, was 100 times more, or 250 x 100 = 25000.00 dollars.
Answer . Kathy's initial investment was $25000.00.
An alloy contains 70% of silver. The amount of silver in the alloy is 1.75 pounds.
Find the weight of the alloy.
You are given that 70% of the alloy mass weights 1.75 pounds.
So you know the part P , which is 1.75 pounds, and the percentage rate (70%).
This is the Type 3 percentage problem .
Apply the formula (***) to find the weight of the alloy.
It is equal to
pounds.
Answer . The weight of the alloy is 2.5 pounds.
Examples of percentage word problems of the Type 1 and the Type 2 are presented in lessons
- Percentage word problems (Type 1 problems: Finding the Part) and
- Percentage word problems (Type 2 problems: Finding the Rate)
in the section Word problems of this site.