smc-4462-25-Comparing quantities using percentages

Percentages, SM-Bank 089

Calculate the percentage discount on an item having a cost price of $45 and a sale price of $30.15. (2 marks)

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$33\text{%}$

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$\text{Discount}$	$=\text{Cost Price}-\text{Sale Price}$
	$=45-30.15$
	$=$14.85$

$\text{Percentage Discount}$	$= \dfrac{\text{Discount}}{\text{Cost price}}\times 100\text{%}$
	$=\dfrac{14.85}{45}\times 100\text{%}$
	$=33\text{%}$

Percentages, SM-Bank 088

Calculate the percentage profit on an item having a cost price of $25 and a sale price of $46.25. (2 marks)

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$85\text{%}$

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$\text{Profit}$	$=\text{Sale Price}-\text{Cost Price}$
	$=46.25-25$
	$=$21.25$

$\text{Percentage Profit}$	$= \dfrac{\text{Profit}}{\text{Cost price}}\times 100\text{%}$
	$=\dfrac{21.25}{25}\times 100\text{%}$
	$=85\text{%}$

Percentages, SM-Bank 087

Iggy bought an e-bike for $3500 in 2022 and sold it in 2023 for $2450 to pay for an overseas holiday.

Calculate the loss that Iggy made. (1 mark)

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Calculate the percentage loss on the original price. (2 marks)

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a. $$1050$

b. $30\%$

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a. $\text{Loss}$

$=3500-2450=$1050$

b. $\text{Percentage Loss}$	$= \dfrac{\text{loss}}{\text{original price}}\times 100\text{%}$
	$=\dfrac{1050}{3500}\times 100\text{%}$
	$=30\%$

Percentages, SM-Bank 085

Mavis bought an original artwork as an investment. She paid $$15\ 400$ in 2018 and sold it in 2023 for $$24\ 024$.

Calculate the profit that Mavis made on her artwork. (1 mark)

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Calculate the percentage profit based on the original price. (2 marks)

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a. $$8624$

b. $56\text{%}$

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a. $\text{Profit}$	$=24\ 024-15\ 400$
	$=$8624$

b. $\text{Percentage Profit}$	$= \dfrac{\text{Profit}}{\text{Original price}}\times 100\text{%}$
	$=\dfrac{8624}{15\ 400}\times 100\text{%}$
	$=56\text{%}$

Percentages, SM-Bank 084

Jeffrey bought a new car for $$35\ 000$ in 2021 and sold it in 2023 for $$21\ 000$.

Calculate the loss that Jeffrey made. (1 mark)

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Calculate the percentage loss on the new car price. (2 marks)

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a. $$14\ 000$

b. $40\%$

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a. $\text{Loss}=35\ 000-21\ 000=$14\ 000$

b. $\text{Percentage Loss}$	$= \dfrac{\text{loss}}{\text{original price}}\times 100\%$
	$=\dfrac{14\ 000}{35\ 000}\times 100\%$
	$=40\%$

Percentages, SM-Bank 078

A coffee shop increases the price of a caramel latte from $4.80 to $6.00.

What is the percentage increase in the price? (2 marks)

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$25\text{%}$

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$\text{Price increase}=6-4.80=$1.20$

$\text{Percentage increase}$	$= \dfrac{1.2}{4.8}\times 100$
	$=0.25\times 100$
	$=25\text{%}$

Percentages, SM-Bank 065

Sachin's cricket bat is pictured below.

The handle of the bat is 29 cm in length.

What is the length of the handle as a percentage of the total length of the bat, to the nearest whole percentage? (2 marks)

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$33\%$

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$\text{Length of the handle as a percentage:}$	$=\dfrac{29}{89.1}\times 100$
	$= 32.54\ldots\%$
	$\approx 33\%$

Percentages, SM-Bank 057 MC

A fishing boat returns with 16 flathead, 7 bream and 9 flounder.

About what percentage of the fish are bream?

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$C$

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$\text{Percentage of bream}$	$=\dfrac{\text{number of bream}}{\text{total fish}}$
	$=\dfrac{7}{16+7+9}$
	$=\dfrac{7}{32}$
	$=0.21875=21.875\%$
	$\approx 22\%$

$\Rightarrow C$

Percentages, SM-Bank 056

In a classroom there are 24 boys and 36 girls.

What percentage of the students in the classroom are girls? (2 marks)

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$60\%$

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$\text{Percentage of girls}$	$=\dfrac{\text{number of girls}}{\text{total students}}=\dfrac{36}{24+36}$
	$=\dfrac{36}{60}=0.6=60\%$

Percentages, SM-Bank 050 MC

Express $18 as a percentage of $600.

$0.03\text{%}$
$2\text{%}$
$3\text{%}$
$6\text{%}$

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$C$

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$\text{Solution}$	$=\dfrac{18}{600}\times 100$
	$=\dfrac{18}{6}$
	$=3\text{%}$

$\Rightarrow C$

Percentages, SM-Bank 045

John uses concrete in his landscaping business.

He makes a dry mix using 1 part cement, 2 parts sand and 3 parts gravel.

Express the amount of gravel as a fraction of the total mix. Give your answer in simplest form. (1 mark)
Express the amount of sand as a percentage of the total mix. (2 marks)
Express the amount of cement compared to the total mix. Give your answer as a recurring decimal. (2 marks)

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a. $\dfrac{1}{2}$

b. $33\dfrac{1}{3}\%$

c. $0.1\dot{6}$

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a. $\text{Gravel as fraction of total}$

$=\dfrac{3}{6}=\dfrac{1}{2}$

b. $\text{Sand as percentage of total}$

$=\dfrac{2}{6}\times 100=\dfrac{1}{3}\times 100=33\dfrac{1}{3}\%$

c. $\text{Cement compared to total}$

$=\dfrac{1}{6}=0.16666\ldots\approx 0.1\dot{6}$

Percentages, SM-Bank 044

Express the number of red building bricks above as:

a fraction of the total number of building bricks, in simplest form. (1 mark)

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a percentage of the total number of building bricks. (1 mark)

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a. $\dfrac{5}{8}$

b. $62.5\%$

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a. $\text{Fraction of total bricks}$

$=\dfrac{5}{8}$

b. $\text{Percentage of total bricks}$	$=\dfrac{5}{8}\times 100=\dfrac{125}{2}$
	$=62.5\%$

Percentages, SM-Bank 043

Express the shaded area above as:

a fraction of the total area, in simplest form. (1 mark)

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a percentage of the total area. (1 mark)

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a. $\dfrac{2}{5}$

b. $40\%$

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a. $\text{Fraction of total area}$

$=\dfrac{4}{10}=\dfrac{2}{5}$

b. $\text{Percentage of total area}$

$=\dfrac{4}{10}\times 100=40\%$

Percentages, SM-Bank 042

Graham has a bag containing coloured marbles.

There are 5 blue marbles, 4 white marbles and 6 green marbles in the bag.

What percentage of the marbles in the bag are blue? Give your answer as a recurring decimal. (2 marks)

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Graham removed 3 blue marbles. What percentage of the remaining marbles are green? (2 marks)

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a. $33.\dot{3}\text{%}$

b. $50\text{%}$

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a. $\text{Total marbles}\ =5+4+6=15$

$\text{Percentage Blue}$	$=\dfrac{5}{15}\times 100$
	$=33.33333…\text{%}$
	$=33.\dot{3}\text{%}$

b. $\text{Total marbles after 3 removed}=12$

$\text{Percentage Green}$	$=\dfrac{6}{12}\times 100$
	$=50\text{%}$

Percentages, SM-Bank 041

Geordie achieved a mark of 31 out of 42 in his English essay.

Convert his mark to a percentage, correct to the nearest whole number. (2 marks)

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$74\text{%}$

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$\text{Conversion}$	$=\dfrac{31}{42}\times 100$
	$=73.809…\text{%}$
	$\approx 74\text{%}$

Percentages, SM-Bank 039

Max wanted to buy a squash racquet that cost $75.

He has saved $60.

How much extra does he need to save as a percentage of the cost price? (2 marks)

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$20\%$

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$\text{Percentage}$	$=\dfrac{15}{75}\times 100=\dfrac{1}{5}\times 100$
	$= 20\%$

$\therefore\ \text{Max needs to save an extra 20%.}$

Percentages, SM-Bank 038

A candy box contains 6 white chocolate bars and 11 dark chocolate bars.

About what percentage of the candy in the box are white chocolate bars? Give your answer to the nearest whole percentage. (2 marks)

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$35\text{%}$

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$\text{Percentage of white chocolate bars}$

$=\dfrac{6}{17}\times 100$

$=35.294….\text{%}$

$\approx 35\text{% (nearest %)}$

Percentages, SM-Bank 037 MC

There were only 17 students in Grace's class on Wednesday. The other 8 were absent.

What percentage of Grace's class was absent?

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$C$

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$\text{Total in class}= 17 + 8= 25$

$\therefore\ \text{Percentage absent}$

$=\dfrac{8}{25}\times 100= 32\%$

$\Rightarrow C$

Percentages, SM-Bank 036 MC

In a water polo season, Vladimir had 330 shots at goal.

He scored 170 goals but missed the rest.

Vladimir's success rate of scoring goals was?

less than 25%
more than 25% but less than 50%
more than 50% but less than 75%
more than 75%

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$C$

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$\text{Success rate}$	$=\dfrac{170}{330}$
	$=0.515…$
	$=52\text{%}$

$\therefore\ \text{His succes rate is more than 50% but less than 75%.}$

$\Rightarrow C$

Percentages, SM-Bank 033 MC

Zoey scored 88% on her Geography exam.

If she achieved the same mark on her French exam, which of these could have been her mark?

$\dfrac{68}{80}$
$\dfrac{45}{50}$
$\dfrac{40}{50}$
$\dfrac{44}{50}$

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$D$

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$88\text{%}$	$=\dfrac{88}{100}$
	$=\dfrac{44}{50}$

$\Rightarrow D$

Percentages, SM-Bank 018

Albert has 50 marbles in his bag.

He records the colour of each marble in the table below.

Marble	Number of Marbles
Blue	20
Red	12
Orange	4
White	?
TOTAL	50

What percentage of the marbles are white? (2 marks)

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$28\%$

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$\text{Number of white marbles}$

$= 50-(20 + 12 + 4)= 14$

$\therefore\ \text{% white}$

$=\dfrac{14}{50}\times 100= 28\%$

Percentages, SM-Bank 017 MC

Which percentage has the same value as $\dfrac{32}{50}$?

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$A$

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$\text{Converting to a percentage:}$

$\dfrac{32}{50} = \dfrac{64}{100} = 64\%$

$\Rightarrow A$

Percentages, SM-Bank 015

A class of 28 students is surveyed. 21 students said they owned a mobile phone.

What percentage of the students surveyed owned a mobile phone? (2 marks)

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$75\%$

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$\text{Percentage}$

$=\dfrac{21}{28}\times 100=\dfrac{3}{4}\times 100= 75\%$

\(\text{Discount}\)	\(=\text{Cost Price}-\text{Sale Price}\)
	\(=45-30.15\)
	\(=$14.85\)

\(\text{Percentage Discount}\)	\(= \dfrac{\text{Discount}}{\text{Cost price}}\times 100\text{%}\)
	\(=\dfrac{14.85}{45}\times 100\text{%}\)
	\(=33\text{%}\)

\(\text{Profit}\)	\(=\text{Sale Price}-\text{Cost Price}\)
	\(=46.25-25\)
	\(=$21.25\)

\(\text{Percentage Profit}\)	\(= \dfrac{\text{Profit}}{\text{Cost price}}\times 100\text{%}\)
	\(=\dfrac{21.25}{25}\times 100\text{%}\)
	\(=85\text{%}\)

b. \(\text{Percentage Loss}\)	\(= \dfrac{\text{loss}}{\text{original price}}\times 100\text{%}\)
	\(=\dfrac{1050}{3500}\times 100\text{%}\)
	\(=30\%\)

a. \(\text{Profit}\)	\(=24\ 024-15\ 400\)
	\(=$8624\)

\(\text{Percentage increase}\)	\(= \dfrac{1.2}{4.8}\times 100\)
	\(=0.25\times 100\)
	\(=25\text{%}\)

\(\text{Length of the handle as a percentage:}\)	\(=\dfrac{29}{89.1}\times 100\)
	\(= 32.54\ldots\%\)
	\(\approx 33\%\)

\(\text{Percentage of bream}\)	\(=\dfrac{\text{number of bream}}{\text{total fish}}\)
	\(=\dfrac{7}{16+7+9}\)
	\(=\dfrac{7}{32}\)
	\(=0.21875=21.875\%\)
	\(\approx 22\%\)