Percent: Word Problems
Basics on the topic Percent: Word Problems
Calculating percent is a very important real world skill. You never know when you will need to calculate the percent of a number, determine the part of a whole, or change a fraction to a percent. For example, what if you found out you could get a 2% rebate on the price you paid for a new laptop, but you would have to write a 2500 word essay to qualify for the rebate.
You might want to find out the amount of the rebate before you write the essay. How do you calculate the percent of a number? Change the percent to a decimal, divide by 100, then multiply the decimal by the number.
How do you determine the part of a whole? If 10% of 50 students apply for the rebate, what is the part or the number of students who apply? Create a proportion with the ratio part : whole set equal to percent : 100 then use cross product to solve for the unknown part. You will need to use the opposite operation to isolate the variable.
For some fractions, raise the terms so there is a 100 in the numerator and the denominator is the percent. For other fractions, divide the numerator by the denominator to calculate a decimal then change the decimal to a percent by multiplying by 100 and adding the percent symbol. To learn some strategies to solve percent problems plus some very interesting statistics, watch this video.
Convert between formats to solve word problems. CCSS.MATH.CONTENT.HSA.SSE.B.3
Transcript Percent: Word Problems
Shannon is searching the Internet for some crime statistics for an article she's writing for her school newspaper. The statistics she found are a lot like word problems with percentages. Let's see what Shannon found out.
Percent Word Problems Example 1
What in the world...? Shannon finds out that five percent of all burglars take a selfie at the place where they commit the crime. Then, they post the picture on social media and are identified. So, If there are 40 burglars, how many of them took a selfie according to the statistics?
In this case, you need to calculate a percentage of the total number of burglars to find out how many of them took selfies.
If you have to find a certain percent of a number, you have to use multiplication. So we know we have to calculate 5% of 40, but first we must transform the percentage into a decimal first.
 This is easy to do: you can write 5% as 5 over 100.
 That is the same as 5 divided by 100, so just move the decimal point two places to the left and you get 0.05.
 Now we multiply 0.05 by 40, giving us 2.
This means: if there are 40 burglars, 2 of them took a selfie.
Percent Word Problems Example 2
Shannon looks at another example. How silly is that?! 6 out of 20 burglars try to break in through the doggy door and have to be freed by firefighters. Let's see what percentage of burglars get caught in doggy doors.
 We can write this as 6 over 20, or 6 divided by 20.
 If we solve this by setting up an equation and using cross multiplication to solve for x. We can write: "6 over 20 is equal to what (x) percent?".
 X % we can write as x over 100. So we get the equation 6 over 20 = x over 100.
 Using cross multiplication, we get 6 · 100 = 20 · x.
 After simplifying that and dividing both sides by 20, we get x = 30.
So this means 30 out of 100 or 30 percent of all burglars try to break in through the doggy door.
Percent Word Problems Example 3
Shannon looks at one last statistic. One out of every hundred thieves tries to blow up a safe to get to the money or jewelry inside. How do we express this as a percentage?
 Out out of every hundred is the same as 1 out of 100, or 1 over 100.
 To transfer this into a percent, you first divide 1 by 100, which is 0.01.
 Now you move the decimal point two places to the right and put a percent sign after it.
So, 1 percent of all thieves try to blow up a safe. But most thieves are not successful.
Percent: Word Problems exercise

Determine how many burglars take a selfie.
HintsDividing by 10, 100, and so on means you move the decimal point in which direction?
$5\div 10=0.5$.
$5~\%$ of $40$ is the same as $5~\% \times 40$.
SolutionIf we know that $5~\%$ of the burglars take a selfie and there are $40$ burglars, how do we calculate the number of burglars taking a selfie?
To solve, we need to calculate a certain percent of a given number.
First change the percentage into a decimal number:
$5~\%=\frac5{100}=0.05$.
Next multiply this decimal number by $40$.
$0.05\times 40=2$
So two out of 40 burglars take a selfie.

Identify the correct percent equation corresponding to the different word problems.
HintsLook at the following equation:
$\Large \frac{\text{ part}}{\text{ whole}}=\frac{\text{ percent}}{100}$.
What information do you have? Manipulate the equation to isolate the unknown variable.
The equation
$\Large \frac{\text{ part}}{\text{ whole}}=\frac{\text{ percent}}{100}$
is equivalent to
$\text{ part}\times 100=\text{ percent}\times \text{ whole}$
using cross multiplication.
SolutionIf we know some of the values, for example the whole and the part or the percentage, we can calculate the unknown value using this formula:
$\large \frac{\text{ part}}{\text{ whole}}=\frac{\text{ percent}}{100}$
$5~\%$ of $40$ burglars take selfies. How many burglars take selfies?
 We know percentage and the whole.
 By multiplying by the whole we get: $5~\%\times 40=0.05\times 40=2$.
 The answer is $2$ out of $40$ burglars take a selfie.
 We know the whole, $20$, and the part of the whole, $6$.
 We transform the equation by multiplying by $100$: $\frac6{20}\times 100=30$.
 The answer is $30~\%$ of $20$ burglars try to break in through the doggy door  incredible.
 We know the whole, $100$, and the part of the whole, $1$.
 We manipulate the equation by multiplying by $100$: $\frac1{100}\times 100=1$.
 The answer is $1~\%$ of all burglars try to blow up a safe.
 We know the part of the whole, $6$, and the percentage, $30$.
 Now we manipulate the equation by cross multiplying $6\times 100=\text{ whole} \times 30$.
 Next we divide by $30$ to get the solution $\frac6{30}\times 100=20$.
 The answer is: $6$ out of $20$ burglars break in through the doggy door.

Analyze each situation and determine the given information.
HintsPercent means out of $100$.
$50~\%=\frac{50}{100}=0.5$
For example: There are 20 dogs playing. Four of them are beagles. What percent are beagles?
$\frac{4}{20}=0.2=20~\%$.
 20 dogs are the whole
 four beagles are the part
 $20$ is the percentage: $20~\%$
SolutionTo use this equation, we need to know two values, so we can calculate the unknown value.
$\large \frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}$
To solve percent problems, understanding the termswhole, part and percent will make it easier to solve problems.
1. Percent equation loving students
 The 20 students who love those equations are the part.
 80 students are the whole.
2. Message sending students
 $40$ is the percentage.
 120 students are the whole.
3. Doggy door burglars
 $20$ is the percentage.
 6 is the part of the whole.

Calculate the new price of the items.
HintsFirst, calculate the amount of the discount then subtract the discount from the original price.
For example $30~\%$ of $100~\$$ are $30~\$$.
The new discounted price is lower than the original price.
SolutionFor these problems, we calculate the unknown part by using the given whole and percentage. We can use the following equation:
$\text{part}=\frac{\text{percent}}{100}\times \text{whole}$.
 Smartphone: the whole is $350~\$$ and the percentage $10$. So the part is $\frac{10}{100}\times 350=35$. This discount has to be subtracted from the original price to get the reduced price: $350~\$35~\$=315~\$$.
 Tennis racket: the whole is $300~\$$ and the percentage $20$. So the part is $\frac{20}{100}\times 300=60$. This discount has to be subtracted from the original price to get the reduced price: $300~\$60~\$=240~\$$.
 Headphones: the whole is $320~\$$ and the percentage $15$. So the part is $\frac{15}{100}\times 320=48$. This discount has to be subtracted from the original price to get the reduced price: $320~\$48~\$=272~\$$.
 Television: the whole is $440~\$$ and the percentage $30$. So the part is $\frac{30}{100}\times 440=132$. This discount has to be subtracted from the original price to get the reduced price: $440~\$132~\$=308~\$$.

Explain the meaning of percent.
HintsDo you know how many cents are in one dollar? Right: 100.
To change a percent into a decimal number, we have to divide. To change a decimal to a percent, we have to multiply.
Remember $0.01=\frac1{100}$.
SolutionIt's important to understand the meaning of percent.
Percent means out of $100$. For example: $5~\%=\frac5{100}=0.05$.
We can change decimals into percent by multiplying by $100$ then writing a $\%$ sign behind it:
$0.05=(0.05\times 100) \%=5~\%$ or $0.01=(0.01\times 100) \%=1~\%$.

Determine the unknown value of each example.
HintsYou can use the equation
$\Large \frac{\text{ part}}{\text{ whole}}=\frac{\text{ percent}}{100}$.
Plug in the known values and isolate the unknown value.
SolutionTo solve percent problems, use this equation:
$\frac{\text{ part}}{\text{ whole}}=\frac{\text{ percent}}{100}$
Penguins:
 percentage: $40 \%$
 the whole: $1200$
 We are looking for the unknown part: $\frac{\text{part}}{1200}=\frac{40}{100}$
 Multiplying by $1200$ leads to the solution: $\text{part}=\frac{40}{100}\times 1200=480$
 So $480$ penguins are female.
 the part: $6$
 the whole $48$
 We are looking for the unknown percentage: $\frac{6}{48}=\frac{\text{percent}}{100}$
 Multiplying with $100$ leads to the solution: $\text{percent}=\frac{6}{48}\times 100=12.5$
 So $12.5~\%$ of the cats are vegetarian.
 percentage: $20 \%$
 the part: $ 8$
 We are looking for the unknown whole: $\frac{8}{\text{whole}}=\frac{20}{100}$
 Cross multiplying leads to: $8\times 100=\text{whole}\times 20$
 Now we divide by $20$ to get: $\text{whole}=\frac{8}{20}\times 100=40$
 So there are $40$ dogs in total.
Thank you for making this lesson so easy to understand! The video played without skipping and I could stay engaged the entire time.