Percent: Word Problems

Percent: Word Problems exercise

• Determine how many burglars take a selfie.

  Hints

  Dividing 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 $5~\% \times 40$.

  Solution

  If 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.

  Hints

  Look 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.

  Solution

  If 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.

  $6$ out of $20$ burglars try to break in through the doggy door.

  • 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.

  Every $100th$ burglar tries to blow up a safe.

  • 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.

  $6$ bulgars try to break in through the doggy door. This is $30\%$ of the burglars. If $6$ break in through the doggy door, how many burglars are there altogther?

  • 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.

  Hints

  Percent 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: $20~\%$

  Solution

  To 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.

  We can calculate the percentage: $\frac{20}{80}=0.25=25~\%$.

  2. Message sending students

  • $40$ is the percentage.
  • 120 students are the whole.

  Now we calculate the part: $40~\%\times 120=0.40\times 120=48$.

  3. Doggy door burglars

  • $20$ is the percentage.
  • 6 is the part of the whole.

  Transforming the equation by cross multiplying we get the whole: $\frac6{20}\times 100=30$.

• Calculate the new price of the items.

  Hints

  First, 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.

  Solution

  For these problems, we calculate the unknown part by using the given whole and percentage. We can use the following equation:

  $\text{part}=\frac{\text{percent}}{100}\times \text{whole}$.

  1. 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: $350~\$-35~\$=315~\$$.
  2. 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: $300~\$-60~\$=240~\$$.
  3. 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: $320~\$-48~\$=272~\$$.
  4. 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.

  Hints

  Do 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 $0.01=\frac1{100}$.

  Solution

  It'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.

  Hints

  You can use the equation

  $\Large \frac{\text{ part}}{\text{ whole}}=\frac{\text{ percent}}{100}$.

  Plug in the known values and isolate the unknown value.

  Solution

  To 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.

  Cats:

  • 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.

  Dogs:

  • 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.