Percent of an Amount – Word Problems 1

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Question 1 of 5

1. Question
`350` pet owners were surveyed on which pet they prefer the most and the results are shown in the pie chart. Using the chart, find out the following:
- `(i) \text(Amount of owners who prefer dogs:)` (147)
  
  `(ii) \text(Amount of owners who prefer birds:)` (49)
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`(i)` Amount of owners who prefer dogs.

According to the pie chart, the amount of pet owners that prefer dogs is `42%` of `350`.

To get the percentage of an amount, simply solve for their product. Use fractions for easier computation.

`42%times350`

`=` `42/100times350/1` Convert values to fraction form

`=` $$\frac{14700}{100}$$

`=` $$\frac{147}{1}$$ Simplify

`=` `147`

Hence, $$\underline{147}$$ of the pet owners prefer dogs.

`(ii)` Amount of owners who prefer birds.

According to the pie chart, the amount of pet owners that prefer birds is `14%` of `350`.

To get the percentage of an amount, simply solve for their product. Use fractions for easier computation.

`14%times350`

`=` `14/100times350/1` Convert values to fraction form

`=` `14/10times35/1` Simplify

`=` $$\frac{490}{10}$$

`=` $$\frac{49}{1}$$ Simplify

`=` `49`

Hence, $$\underline{49}$$ of the pet owners prefer birds.

`(i) 147`

`(ii) 49`

Question 2 of 5

2. Question

A large bottle holds `5` litres of water. What percentage of water remains after it fills four `250 \text(ml)` cups with water?

(80)`%`

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Percentage of Change

$$\%\mathsf{change=\frac{\color{#D800AD}{change}}{\color{#00880A}{original}}\times\frac{100}{1}}$$

First, visualise and summarise the data given in the problem

Note that the `1` litre `=1000 \text(ml)`

Now, find how much water remains in the bottle

remaining water	`=`	total water `-` water poured to cups
	`=`	`5000 \text(ml)``-(4` cups`xx``250 \text(ml))`
	`=`	`5000-1000`
	`=`	`4000 \text(ml)`

The bottle has `4000 \text(ml)` remaining water

Finally, find the percentage of the remaining water using the formula

change (remaining water)`=4000 \text(ml)`

original (total water)`=5000 \text(ml)`

$$\%\mathsf{change}$$	`=`	$$\mathsf{\frac{\color{#D800AD}{change}}{\color{#00880A}{original}}\times\frac{100}{1}}$$

	`=`	$$\frac{\color{#D800AD}{4000}}{\color{#00880A}{5000}}\times\frac{100}{1}$$

	`=`	$$\frac{4}{5}\times\frac{100}{1}$$	Cancel the zeros

	`=`	$$\frac{400}{5}$$

	`=`	$$80\%$$

`80%` of the water remains in the bottle

`80%`

Question 3 of 5

3. Question

A box contains `27` apples. If `66 2/3%` of the apples are red, how many green apples are there?

(9) `\text(green apples)`

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Transforming a Fraction from Mixed to Improper

`=`

$$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$

First, list down the known values.

`\text(Total number of apples)=27`

`\text(Percentage of red apples)=66 2/3%`

Next, change the percentage into an improper fraction by multiplying the denominator by the whole number and then adding the numerator

$$\color{#00880A}{66}\frac{\color{#007DDC}{2}}{\color{#9a00c7}{3}}$$	`=`	$$\frac{(\color{#9a00c7}{3}\times\color{#00880A}{66})+\color{#007DDC}{2}}{\color{#9a00c7}{3}}$$

	`=`	$$\frac{198+2}{3}$$

	`=`	$$\frac{200}{3}\%$$

Then, convert the percentage to a fraction by having `100` as the percentage value’s denominator

Dividing fractions is the same as multiplying the dividend by the divisor’s reciprocal

`\text(Fraction)`	`=`	$$\frac{\frac{200}{3}}{\color{#CC0000}{100}}$$

	`=`	$$\frac{200}{3}\div{\color{#CC0000}{100}}$$	Change from a fraction to division

	`=`	$$\frac{200}{3}\times\frac{1}{100}$$	Get the divisor’s reciprocal then multiply

	`=`	$$\frac{2}{3}$$	Simplify

Finally, to get the percentage of an amount, simply solve for their product. Use fractions for easier computation.

	`2/3``times``27`

`=`	`2/3times27/1`	Convert values to fraction form

`=`	`2/1times9/1`	Simplify

`=`	$$\frac{18}{1}$$

`=`	`18`

Hence, there are $$\underline{18\;\text{red apples}}$$.

To solve for number of green apples, subtract the number of red apples from the total number of apples

`\text(Green apples)`	`=`	$$27-18$$
	`=`	$$9$$

`9 \text(green apples)`

Question 4 of 5

4. Question
A real estate agent gets `3.5%` commission on the first $$$80{,}000$$ on the value of a home and he gets an additional `2%` commission for the remaining balance. How much commission in total will he earn if he sells a home valued at $$$420{,}000$$?
- `$` (9600)
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A commission is expressed as a percentage of the value of goods sold.

First, draw a line diagram to further understand the given values.

Solve for the remaining balance by subtracting $$$80{,}000$$ from the value of the house, which is $$$420{,}000$$.

`\text(Remaining Balance)` `=` $$$420{,}000-80{,}000$$

`=` $$$340{,}000$$

Next, solve the commission for the first $$$80{,}000$$ of the value, which will be `3.5%`.

$$$3.5\%\times80{,}000$$

`=` $$\frac{3.5}{100}\times\frac{80{,}000}{1}$$ Convert values to fraction form

`=` $$$0.035\times80{,}000$$ Simplify

`=` `$2800`

Then, solve the commission for the rest of the value, which will be `2%`.

$$$2\%\times340{,}000$$

`=` $$\frac{2}{100}\times\frac{340{,}000}{1}$$ Convert values to fraction form

`=` $$$0.02\times340{,}000$$ Simplify

`=` `$6800`

Finally, add the two commissions to get the total commission

`\text(Total Commission)` `=` `2800``+``6800`

`=` `$9600`

Hence, the real estate agent will get a total commission of $$\underline{$9600}$$.

`$9600`
Question 5 of 5

5. Question
During a `30 \text(km)` marathon race, Jason injured his ankle just as he completed `80%` of the race. How far from the end did he get injured?
- (6) `\text(km)`
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First, summarise the data and draw a diagram for easier understanding of the problem

`\text(Total distance)=30 \text(km)`

`\text(Percentage that Jason finished)=80%`

`\text(Percentage of total distance)=100%`

`\text(Percentage of remaining distance)=?`

Next, find the percentage of the remaining distance.

Do this by subtracting the percentage of the marathon Jason finished `(80%)` from `100%`

`% \text(of remaining distance)` `=` `100``-``80`

`=` `20%`

There is `20%` of the marathon left for Jason.

Finally, multiply the percentage to the total distance of the marathon which is `30`

`\text(Remaining distance)` `=` `20%``times``30`

`=` `20/100times30/1` Convert values to fraction form

`=` `2/1times3/1` Simplify

`=` $$\frac{2\times3}{1}$$

`=` `6`

Hence, Jason has $$\underline{6\;\text{km}}$$ left to finish the marathon.

`6 \text(km)`

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Depreciation

	`42%times350`

`=`	`42/100times350/1`	Convert values to fraction form

`=`	$$\frac{14700}{100}$$

`=`	$$\frac{147}{1}$$	Simplify

`=`	`147`

	`14%times350`

`=`	`14/100times350/1`	Convert values to fraction form

`=`	`14/10times35/1`	Simplify

`=`	$$\frac{490}{10}$$

`=`	$$\frac{49}{1}$$	Simplify

`=`	`49`

`\text(Remaining Balance)`	`=`	$$$420{,}000-80{,}000$$
	`=`	$$$340{,}000$$

	$$$3.5\%\times80{,}000$$

`=`	$$\frac{3.5}{100}\times\frac{80{,}000}{1}$$	Convert values to fraction form

`=`	$$$0.035\times80{,}000$$	Simplify
`=`	`$2800`

	$$$2\%\times340{,}000$$

`=`	$$\frac{2}{100}\times\frac{340{,}000}{1}$$	Convert values to fraction form

`=`	$$$0.02\times340{,}000$$	Simplify
`=`	`$6800`

`\text(Remaining distance)`	`=`	`20%``times``30`

	`=`	`20/100times30/1`	Convert values to fraction form

	`=`	`2/1times3/1`	Simplify

	`=`	$$\frac{2\times3}{1}$$

	`=`	`6`

`\text(Total Commission)`	`=`	`2800``+``6800`
	`=`	`$9600`

Percent of an Amount – Word Problems 1

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Quiz summary

Information

1. Question

Hint

Well Done!

2. Question

Hint

Keep Going!

Percentage of Change

3. Question

Hint

Nice Job!

Transforming a Fraction from Mixed to Improper

4. Question

Hint

Correct!

5. Question

Hint

Fantastic!

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