Percent of an Amount – Word Problems 1

Question 1 of 5

350

$350$ 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:

$(i) Amount of owners who prefer dogs:$ $(i) \text(Amount of owners who prefer dogs:)$ (147)

$(i i) Amount of owners who prefer birds:$ $(ii) \text(Amount of owners who prefer birds:)$ (49)

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(i)

$(i)$ Amount of owners who prefer dogs.

According to the pie chart, the amount of pet owners that prefer dogs is

42 %

$42%$ of

350

$350$ .

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

	$42 % \times 350$ $42%times350$

$=$ $=$	$\frac{42}{100} \times \frac{350}{1}$ $42/100times350/1$	Convert values to fraction form

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

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

$=$ $=$	$147$ $147$

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

(i i)

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

According to the pie chart, the amount of pet owners that prefer birds is

14 %

$14%$ of

350

$350$ .

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

	$14 % \times 350$ $14%times350$

$=$ $=$	$\frac{14}{100} \times \frac{350}{1}$ $14/100times350/1$	Convert values to fraction form

$=$ $=$	$\frac{14}{10} \times \frac{35}{1}$ $14/10times35/1$	Simplify

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

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

$=$ $=$	$49$ $49$

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

(i) 147

$(i) 147$

(i i) 49

$(ii) 49$

Question 2 of 5

A large bottle holds

5

$5$ litres of water. What percentage of water remains after it fills four

250 ml

$250 \text(ml)$ 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

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

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

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.

$6 \text(km)$

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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