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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:
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`(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` -
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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 problemNote that the `1` litre `=1000 \text(ml)`
Now, find how much water remains in the bottleremaining 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 waterFinally, find the percentage of the remaining water using the formulachange (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 denominatorDividing 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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