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Percentages, SM-Bank 067

Fred owns a property which is currently experiencing a drought. 

Fred's dam is currently 30% below its maximum capacity.

Calculate the capacity of the dam when full if it currently holds \(280\ 000\) litres?  (2 marks)

Show Answers Only

\(400\ 000\ \text{litres}\)

Show Worked Solution

\(\text{Capacity has decreased by 30%.}\)

\(\therefore\ 280\ 000\ \text{litres represents}\ \dfrac{70}{100}\ \text{of the full capacity}\)

\(\therefore\ \dfrac{7}{10}\ \times\ \text{Full capacity}\) \(=280\ 000\)
\(\therefore\ \text{Full capacity}\) \(=\dfrac{280\ 000\times 10}{7}=400\ 000\ \text{litres}\)

Percentages, MS-Bank 066

Asti bought a formal dress that was on sale at a 75% discount.

Calculate the original price of the formal dress if the sale price was $60?  (2 marks)

Show Answers Only

\($240\)

Show Worked Solution

\(\text{Dress has been discounted by 75%.}\)

\(\therefore\ $60\ \text{represents}\ \dfrac{1}{4}\ \text{of the original price.}\)

\(\therefore\ \dfrac{1}{4}\ \times\ \text{Original Price}\) \(=60\)
\(\therefore\ \text{Original Price}\) \(=60\times 4=$240\)

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)

Show Answers Only

\(33\%\)

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

 

Percentages, SM-Bank 064 MC

Bec is buying 40 kilograms of dry dog food for her bullmastiff.

The table below lists the original price and the amount of discount on a 40 kilogram bag of dry dog food at four different pet stores.

40 kg Dry Dog Food Prices
Shop Original price Discount
A. \($220\) \(18\text{%}\)
B. \($245\) \(25\text{%}\)
C. \($250\) \(\dfrac{1}{5}\)
D. \($230\) \($35\text{ off}\)

Which shop has the lowest sale price for the jeans?

Show Answers Only

\(A\)

Show Worked Solution

\(\text{Consider the sale price at each shop:}\)

\(\text{A}\) \(= 220-(18\text{%}\times 220)=220-39.60= $180.40\)
\(\text{B}\) \(= 245-(25\text{%}\times 245) = 245-61.25 =$183.75\)
\(\text{C}\) \(= 250-(\dfrac{1}{5}\times 250) = 250-50= $200\)
\(\text{D}\) \(= 230-35 = $195\)

   
\(\therefore\ \text{Shop }A\text{ has the lowest sale price.}\)

\(\Rightarrow A\)

Percentages, SM-Bank 063

Jye was checking his phone battery usage and found he spent his time listening to music, using social media and viewing YouTube videos.

Last week he spent 25 hours in total using his phone and the pie chart below shows the breakdown of his usage.

 

How much time did Jye spend on social media?  (2 marks)

Show Answers Only

\(5\ \text{hours}\)

Show Worked Solution
\(\text{Percentage watching YouTube videos}\) \(=\dfrac{8}{25} \times 100\)
  \(=32\text{%}\)

  

\(\text{Percentage on social media}=100-(48+32)=20\text{%}\)

\(\therefore\ \text{Amount of usage on social media}\) \(=20\text{%}\times 25\)
  \(=5\ \text{hours}\)

 

Percentages, SM-Bank 062

Joy set up a cardio gym in her garage and purchased a treadmill, a rowing machine and a spin bike.

She spent $6000 in total and the pie chart below shows how she spent it.

How much money did Joy spend on the spin bike?  (2 marks)

Show Answers Only

\($1860\)

Show Worked Solution
\(\text{Percentage spent on the treadmill}\) \(=\dfrac{2460}{6000} \times 100\)
  \(=41\text{%}\)

  

\(\text{Percentage on spin bike}=100-(41+28)=31\text{%}\)

\(\therefore\ \text{Amount spent on spin bike}\) \(=31\text{%}\times 6000\)
  \(=31\times 60\)
  \(=$1860\)

 

Percentages, SM-Bank 061

A ring has a normal price tag of $320.

At sale time, it is reduced by 30%.

What it the sale price of the ring? (2 marks)

Show Answers Only

\($224\)

Show Worked Solution

\(\text{Method 1}\)

\(\text{Sale price of ring}\) \(=320-320\times 30\text{%}\)
  \(=320-32\times 3\)
  \(=320-96\)
  \(=$224\)

  

\(\text{Method 2 (Advanced)}\)

\(\text{Sale price of ring}\) \(=320\times (100-30)\text{%}\)
  \(=320\times 70\text{%}\)
  \(=32\times 7\)
  \(=$224\)

 

Percentages, SM-Bank 060

A watch has a normal price tag of $240.

At sale time, it is reduced by 25%.

What it the sale price of the watch? (2 marks)

Show Answers Only

\($180\)

Show Worked Solution

\(\text{Method 1}\)

\(\text{Sale price of watch}\) \(=240-240\times 25\text{%}\)
  \(=240-60\)
  \(=$180\)

  

\(\text{Method 2 (Advanced)}\)

\(\text{Sale price of watch}\) \(=240\times (100-25)\text{%}\)
  \(=240\times 75\text{%}\)
  \(=240\times \dfrac{3}{4}\)
  \(=$180\)

 

Percentages, SM-Bank 059

A tree was 15 metres tall two years ago. 

It was measured this year and its height had increased by 64%.

How tall is the tree now?  (2 marks)

Show Answers Only

\(24.6\ \text{metres}\)

Show Worked Solution

\(\text{Method 1}\)

\(\text{Height of tree}\) \(=15 + 15\times 64\%=15+9.6\)
  \(=24.6\ \text{metres}\)

  

\(\text{Method 2 (Advanced)}\)

\(\text{Height of tree}\) \(=15\times 164\%=15\times 1.64\)
  \(=24.6\ \text{metres}\)

 

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?

  1. 50%
  2. 28%
  3. 22%
  4. 21%
Show Answers Only

\(C\)

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

  
\(\Rightarrow C\)

 

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)

Show Answers Only

\(60\%\)

Show Worked Solution
\(\text{Percentage of girls}\) \(=\dfrac{\text{number of girls}}{\text{total students}}=\dfrac{36}{24+36}\)
  \(=\dfrac{36}{60}=0.6=60\%\)

  

Percentages, SM-Bank 055

Barry weighed 80 kg and started doing triathlons.

He lost 2.8 kg in the 1st month, 3 kg in the 2nd month and 2.2 kg in the 3rd month.

What percentage of his original weight did Barry lose?  (2 marks)

Show Answers Only

\(10\text{%}\)

Show Worked Solution
\(\text{Total kilograms lost}\) \(=2.8+3+2.2=8.0\)

  

\(\text{Percentage of original weight lost}\) \(=\dfrac{8}{80}\times 100=0.1\times 100\)
  \(=10\text{%}\)

Percentages, SM-Bank 054

Gerry is streaming his favourite show on Paraflix.

Each episode is usually 50 minutes long.

Gerry keeps losing his internet connection and it takes 30% longer to watch tonight's episode.

How long did it take Gerry to watch tonight's episode?  (2 marks)

Show Answers Only

\(65\text{ minutes}\)

Show Worked Solution

\(\text{Solution 1}\)

\(\text{Time}\) \(=50+(30\text{%} \times 50)=50+15\)
  \(=65\ \text{minutes}\)

  
\(\text{Solution 2 (Advanced)}\)

\(\text{Time}\) \(=50\times 1.3=65\ \text{minutes}\)

Percentages, SM-Bank 053

A pot weighed 12 kg when empty. 

When filled with garden soil and plants, the pot weighs 35% more than when empty.

How much does the filled pot weigh?  (2 marks)

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\(16.2\text{ kilograms}\)

Show Worked Solution

\(\text{Solution 1}\)

\(\text{Weight}\) \(=12+(12\times 35\%=12+4.2\)
  \(=16.2\ \text{kilograms}\)

\(\text{Solution 2}\)

\(\text{Weight}\) \(=12\times 1.35=16.2\ \text{kilograms}\)

Percentages, SM-Bank 052 MC

Which set of numbers is arranged from the smallest to the largest?

  1. \(-6\ ,\ -7\ ,\ 80\text{%}\ ,\ \dfrac{5}{3}\)
  2. \(-7\ ,\ -6\ ,\ 80\text{%}\ ,\ \dfrac{5}{3}\)
  3. \(-6\ ,\ -7\ ,\ \dfrac{5}{3}\ ,\ 80\text{%}\)
  4. \(-7\ ,\ -6\ ,\ \dfrac{5}{3}\ ,\ 80\text{%}\)
Show Answers Only

\(B\)

Show Worked Solution

\(-7\text{ is less than}\ -6\)

\(80\text{%} = \dfrac{4}{5}\ \text{which is less than}\ \dfrac{5}{3}\)

\(\therefore\ \text{Smallest to largest is }\rightarrow -7\ ,\ -6\ ,\ 80\text{%}\ ,\ \dfrac{5}{3}\)

\(\Rightarrow B\)

Percentages, SM-Bank 051 MC

Which set of numbers is arranged from the smallest to the largest?

  1. \(-3\ ,\ -2\ ,\ 25\text{%}\ ,\ \dfrac{5}{4}\)
  2. \(-2\ ,\ -3\ ,\ 25\text{%}\ ,\ \dfrac{5}{4}\)
  3. \(-3\ ,\ -2\ ,\ \dfrac{5}{4}\ ,\ 25\text{%}\)
  4. \(-2\ ,\ -3\ ,\ \dfrac{5}{4}\ ,\ 25\text{%}\)
Show Answers Only

\(A\)

Show Worked Solution

\(-3\text{ is less than}\ -2\)

\(25\text{%} = \dfrac{1}{4}\ \text{which is less than}\ \dfrac{5}{4}\)

\(\therefore\ \text{Smallest to largest is }\rightarrow -3\ ,\ -2\ ,\ 25\text{%}\ ,\ \dfrac{5}{4}\)

\(\Rightarrow A\)

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.

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

 

Show Answers Only

a.     \(\dfrac{1}{2}\)

b.     \(33\dfrac{1}{3}\%\)

c.     \(0.1\dot{6}\)

Show Worked Solution
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:

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

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

 

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a.     \(\dfrac{5}{8}\)

b.     \(62.5\%\)

Show Worked Solution
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:

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

  2. a percentage of the total area.  (1 mark)

 

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a.     \(\dfrac{2}{5}\)

b.     \(40\%\)

Show Worked Solution
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.

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

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

 

Show Answers Only

a.     \(33.\dot{3}\text{%}\)

b.     \(50\text{%}\)

Show Worked Solution

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)

 

Show Answers Only

\(74\text{%}\)

Show Worked Solution
\(\text{Conversion}\) \(=\dfrac{31}{42}\times 100\)
  \(=73.809…\text{%}\)
  \(\approx 74\text{%}\)

Percentages, SM-Bank 040 MC

The population of Australian states in 2015 and 2016 is recorded in the table below.

Some data for Western Australia is not shown.
 

 
What was the population of Western Australia (WA) close to in 2016?

  1. \(2\ 773\ 100\)
  2. \(2\ 710\ 500\)
  3. \(2\ 147\ 600\)
  4. \(2\ 091\ 300\)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Solution 1}\)

\(\text{WA Population in 2016}\)

\(= 2\ 085\ 021 + \Big(\dfrac{0.3}{100}\times 2\ 085\ 021\Big)=2\ 085\ 021 + 6255.063\)

\(=2\ 091\ 276.063\approx 2\ 091\ 300\)

 

\(\text{Solution 2 (Advanced)}\)

\(\text{WA Population in 2016}\)

\(=2\ 085\ 021\times 100.3\%= 2\ 085\ 021\times 1.003\)

\(\approx 2\ 091\ 300\)

 
\(\Rightarrow D\)

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)

Show Answers Only

\(20\%\)

Show Worked Solution
\(\text{Percentage}\) \(=\dfrac{15}{75}\times 100=\dfrac{1}{5}\times 100\)
  \(= 20\%\)

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

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)

Show Answers Only

\(35\text{%}\)

Show Worked Solution

\(\text{Percentage of white chocolate bars}\)

\(=\dfrac{6}{17}\times 100\)

\(=35.294….\text{%}\)

\(\approx 35\text{%   (nearest %)}\)

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?

  1. less than 25%
  2. more than 25% but less than 50%
  3. more than 50% but less than 75%
  4. more than 75%
Show Answers Only

\(C\)

Show Worked Solution
\(\text{Success rate}\) \(=\dfrac{170}{330}\)
  \(=0.515…\)
  \(=52\text{%}\)

 

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

 
\(\Rightarrow C\)

Percentages, SM-Bank 035

Ricky wants to buy a cricket bat that has a normal price of $160.

He is given a 15% discount.

What is the value of the discount?  (2 marks)

Show Answers Only

\($24\)

Show Worked Solution

\(\text{Value of the discount}\)

\(10\text{% of }160 = 16\)

\(\therefore\ 5\text{% of }160=8\)

\(\therefore\ 15\text{% of }160=16 + 8 =24\)

\(\therefore\ \text{The value of the discount was }$24.\)

Percentages, SM-Bank 034 MC

Hoon's camera has a memory card that holds 20 gigabytes.

He has used exactly 16 gigabytes of memory.

What percentage of the memory has not been used?

  1. \(4\text{%}\)
  2. \(20\text{%}\)
  3. \(25\text{%}\)
  4. \(80\text{%}\)
Show Answers Only

\(B\)

Show Worked Solution
\(\text{Memory left}\) \(= 20-16\)
  \(= 4\ \text{GB}\)

 

\(\therefore\ \text{Percentage not used}\)

\(=\dfrac{4}{20}\)

\(= 20\text{%}\)

 
\(\Rightarrow B\)

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?

  1. \(\dfrac{68}{80}\)
  2. \(\dfrac{45}{50}\)
  3. \(\dfrac{40}{50}\)
  4. \(\dfrac{44}{50}\)
Show Answers Only

\(D\)

Show Worked Solution
\(88\text{%}\) \(=\dfrac{88}{100}\)
  \(=\dfrac{44}{50}\)

 
\(\Rightarrow D\)

Percentages, SM-Bank 032 MC

Santana is buying a guitar string.

Some of the strings are on sale.

Select the string that will be cheapest.

A. B. C. D.

 

Show Answers Only

\(C\)

Show Worked Solution

\(\text{C}\text{ost of each option:}\)

\(\text{A.  }$17\)

\(\text{B.  }$35\ \text{less }50\text{%} = $17.50\)

\(\text{C.  }$20\ \text{less }20\text{%} = 20-4 = $16\)

\(\text{D.  }$24\ \text{less } 25\text{%} = 24-6 = $18\)

\(\therefore\ \text{Sale: take }20\text{% off is the cheapest string.}\)

\(\Rightarrow C\)

Percentages, SM-Bank 031

A local soccer club has 1600 fans.

At a game, one-quarter of the fans wear a yellow jersey and the rest wear red.

25% of the red jerseys have a black stripe down the back.

How many red jerseys have a black stripe?  (2 marks)

Show Answers Only

\(300\)

Show Worked Solution
\(\text{Total red jerseys}\) \(=75\text{%}\times 1600\)
  \(=\dfrac{3}{4}\times 1600=1200\)

 

\(\therefore\ \text{Red jerseys with black stripe}\)
\(=0.25\times 1200=300\)

Percentages, SM-Bank 030

Marty and Paul swam 3 kilometres in an ocean swimming race.

Marty finished in a time of 1 hour and 10 minutes.

Paul took 25% longer than Marty.

How long did Paul take to finish the race?  (2 marks)

Show Answers Only

\(87.5\ \text{minutes}\)

Show Worked Solution

\(\text{Solution 1}\)

\(\text{Paul’s time}\) \(=1\ \text{hour and 10 minutes}+(25\%\times 1\ \text{hour and 10 minutes})\)
  \(=70+17.5\)
  \(=87.5\ \text{minutes}\)

 

\(\text{Solution 2 (Advanced)}\)

\(\text{Paul’s time}\)

\(= (1\ \text{hour and 10 minutes})\times 125\%\)

\(= 70\times 1.25\)

\(= 87.5\ \text{minutes}\)
 

\(\therefore\ \text{Paul took 87.5 minutes to complete the race.}\)

Percentages, SM-Bank 029

Jake bought a mobile phone at 25% off the original price.

The original price was $380.

How much did Jake pay for the mobile phone?  (2 marks)

Show Answers Only

\($285\)

Show Worked Solution

\(\text{Solution 1}\)

\(\text{Price of mobile}\) \(=380-(25\%\times 380)=380-95\)
  \(=$285\)

 

\(\text{Solution 2 (Advanced)}\)

\(\text{Price of mobile}\) \(=0.75\times 380=$285\)

Percentages, SM-Bank 027

Richard bought a second hand snowboard at a cost of $390.

Richard had to spend 65% of his savings to buy the snowboard.

How much did Richard have in his savings after buying the snowboard?  (2 marks)

Show Answers Only

\($210\)

Show Worked Solution
\(65\text{%}\times \text{Savings}\) \(= $390\)
 \(\therefore\ \text{Savings}\) \(=\dfrac{390}{0.65}= $600\)

 

\(\therefore\ \text{Savings left}\) \(= 600-390= $210\)

Percentages, SM-Bank 026

Harrison was saving his money to buy a cricket bat.

After 1 month, he had saved 45% of the bat's cost.

After 2 months, he had saved another $90 and now had 75% of the bat's cost.

How much does the bat cost?  (2 marks)

Show Answers Only

\($300\)

Show Worked Solution
\(75\%-45\%\) \(= $90\)
\(30\%\) \(= $90\)
\(\therefore\ 1\%\) \(= $3\)

 

\(\therefore\ \text{The bat cost}\) \(= 100\times 3= $300\)

Percentages, SM-Bank 025

Michael purchases a 3D printer worth $2 490 000.

He was given a 10% discount.

What was the price paid by Michael after the discount?  (2 marks)

Show Answers Only

\($2\ 241\ 000\)

Show Worked Solution

\(\text{Solution 1}\)

\(\text{Discount}\) \(= 10\text{%}\times 2\ 490\ 000\)
  \(= $249\ 000\)

 

\(\therefore\ \text{Discounted Price}\) \(= 2\ 490\ 000-249\ 000\)
  \(= $ 2\ 241\ 000\)

 

\(\text{Solution 2 (Advanced)}\)

\(\text{Discounted Price}\) \(= 90\%\times 2\ 490\ 000=0.9\times 2\ 490\ 000\)
  \(= $ 2\ 241\ 000\)

Percentages, SM-Bank 024

A box of golf balls normally cost $19.50.

During a sale, the golf shop took 10% off the regular price of the balls.

What is the new sale price of the golf balls?  (2 marks)

Show Answers Only

\($17.55\)

Show Worked Solution
\(10\text{% discount}\) \(=\dfrac{19.50}{10}= $1.95\)

 

\(\therefore\ \text{Sale price}\) \(= $19.50-$1.95= $17.55\)

Percentages, SM-Bank 023

Don buys a cricket ball, originally marked $30, that is discounted by 25%.

He also has a loyalty card that gives him another 20% off the sale price.

What is the final cost of the ball?   (2 marks)

Show Answers Only

\($18\)

Show Worked Solution

\(\text{Solution 1}\)

\(\text{Sale price}\) \(= 30-(25\%\times 30)30-7.50= $22.50\)

 

\(\therefore\ \text{Final cost}\) \(= 22.50-(20\%\times 22.50=22.50-4.50)\)
  \(= $18\)

 

\(\text{Solution 2 (Advanced)}\)

\(\text{Final cost}\) \(= 30\times 0.75\times 0.8= $18\)

Percentages, SM-Bank 022

Walker is doing an intensive swim program over the summer holidays.

In his first session, he swims 50 laps.

In his second session, he swims 30% more laps than his first session.

In his third session, he swims 20% more laps than his second session.

How many laps does he swim at his third practice?  (2 marks)

Show Answers Only

\(78\ \text{laps}\)

Show Worked Solution

\(\text{1st session} = 50\ \text{laps}\)

\(\text{2nd session}\) \(= 50 + (30\text{%}\times 50)\)
  \(= 50 + 15\)
  \(= 65\ \text{laps}\)

 

\(\text{3rd session}\) \(= 65 + (20\text{%}\times 65)\)
  \(= 65 + 13\)
  \(= 78\ \text{laps}\)

Percentages, SM-Bank 021

A sport store has a sale.
 

What is the difference in the sale prices of these two tents?  (2 marks)

Show Answers Only

\($7.50\)

Show Worked Solution
\(\text{Price of tent 1}\) \(= 85-30\%\times 85\)
  \(= 85-25.5\)
  \(= $59.50\)
\(\text{Price of tent 2}\) \(= 80-35\%\times 80\)
  \(= 80-28.0\)
  \(= $52.00\)

  

\(\therefore\ \text{Price difference}\) \(= 59.50-52\)
  \(= $7.50\)

Percentages, SM-Bank 020

Mary has 60 books and splits them into four categories.

This table shows the percentage of each category.
  

Book Category Percentage
Textbooks 35%
Sport 30%
Fiction 20%
Travel 15%

 

How many sport books does Mary have?  (2 marks)

Show Answers Only

\(18\)

Show Worked Solution

\(\text{30% of 60 books are sport books.}\)

\(\therefore\ \text{Number of sport books}\) \(= 30\text{%}\times 60\)
  \(=\dfrac{3}{10}\times 60\)
  \(= 18\text{ books}\)

Percentages, SM-Bank 019

A scholarship fund of $1 000 000 is allocated between three scholarships as shown in the table below.
  

  Percentage of $1 million
Academic Scholarship 40%
Sport Scholarship 30%
Hardship Scholarship 30%

  
150 students were given a Hardship Scholarship.

How much did each Hardship Scholarship winner receive?  (2 marks)

Show Answers Only

\($2000\)

Show Worked Solution

\(\text{Hardship Scholarship Funds}\)

\(= 30\text{%}\times 1\ 000\ 000\)

\(= $300\ 000\)
 

\(\therefore\ \text{Amount each winner received}\)

\(= \dfrac{300\ 000}{150}\)

\(= $2000\)

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)

Show Answers Only

\(28\%\)

Show Worked Solution

\(\text{Number of white marbles}\)

\(= 50-(20 + 12 + 4)= 14\)
   

\(\therefore\ \text{% white}\) \(=\dfrac{14}{50}\times 100= 28\%\)

Percentages, SM-Bank 016 MC

The table below lists the original price and the amount of discount of a pair of jeans at four different shops.
    

JEANS SALE
Shop Original price Discount
A. \($20\) \(25\%\)
B. \($21\) \(\dfrac{1}{3}\)
C. \($18\) \(20\%\)
D. \($17\) \($2\text{ off}\)

    
Which shop has the lowest sale price for the jeans?

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\(B\)

Show Worked Solution

\(\text{Consider the sale price at each shop:}\)

\(\text{A}\) \(= 20-(25\%\times 20) = $15\)
\(\text{B}\) \(= 21-(1/3\times 21) = $14\)
\(\text{C}\) \(= 18-(20 \text{%}\times 18) = $14.40\)
\(\text{D}\) \(= 17-2 = $15\)

 
\(\Rightarrow B\)

Percentages, SM-Bank 014

Gary is painting his house over 3 days.

    • He paints \(\dfrac{1}{3}\) of the house on the first day.
    • He paints \(\dfrac{5}{12}\) of the house on the second day.

In order to finish, what percentage of the house does Gary need to paint on the third day?  (2 marks)

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\(25\%\)

Show Worked Solution
\(\text{Fraction painted}\) \(=\dfrac{1}{3}+\dfrac{5}{12}=\dfrac{4 + 5}{12}\)
  \(=\dfrac{9}{12}=\dfrac{3}{4}=75\%\)

 
\(\therefore\ 25\text{% needs to be painted on the third day.}\)

Percentages, SM-Bank 013

Find:

  1. 2% of $14.50.  (2 mark)

  2. 15% of 300 kg.  (2 marks)

  3. \(12\dfrac{1}{2}\%\) of 880 km.  (2 marks)

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a.     \($0.29\)

b.     \(45\ \text{kg}\)

c.     \(110\ \text{km}\)

Show Worked Solution
a.    \(1\%\ \text{of}\ $14.50\) \(=$0.145\)
\(\therefore\ 2\%\ \text{of}\ $14.50\) \(=2\times $0.145=$0.29\)

 

b.     \(15\%\ \text{of}\ 300\text{ kg}\)  
\(10\text{% of }\ 300\ \text{kg}\) \(=30\ \text{kg}\)
\(\therefore\ 5\text{% of }\ 300\ \text{kg}\) \(=15\ \text{kg}\)
\(\therefore\ 15\text{% of }\ 300\ \text{kg}\) \(=30+15=45\ \text{kg}\)

 

c.     \(12\dfrac{1}{2}\text{% of}\ 880\ \text{km}\)  
 \(25\text{% of}\ 880\ \text{km}\)  \(=220\ \text{km}\)
 \(\therefore\ 12\dfrac{1}{2}\text{% of}\ 880\ \text{km}\) \(=110\ \text{km}\)

Percentages, SM-Bank 012

Find:

  1. 10% of $325.  (1 mark)

  2. 30% of 1200 kg.  (2 marks)

  3. 75% of 500 km.  (2 marks)

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a.     \($32.50\)

b.     \(360\text{ kg}\)

c.     \(375\text{ km}\)

Show Worked Solution
a.    \(10\text{% of}\ $325\) \(=\dfrac{10}{100}\times 325=\dfrac{1}{10}\times 325\)
  \(=$32.50\)

 

b.     \(30\text{% of }1200\text{ kg}\) \(=\dfrac{30}{100}\times 1200=30\times 12\)
  \(=360\ \text{kg}\)

 

c.     \(75\text{% of}\ 500\) \(=\dfrac{75}{100}\times 500=75\times 5\)
  \(=375\ \text{km}\)

Percentages, SM-Bank 011

Brittany is an apprentice hair dresser who works 8 hours per day.

Yesterday she spent her time in the following way.

    • 0.42 of her day \(\rightarrow\) sweeping and tidying the salon
    • 0.18 of her day \(\rightarrow\) washing hair
    • 0.05 of her day \(\rightarrow\) drying hair

The rest of Brittany's day was spent restocking the shelves with new products.

What percentage of Brittany's day was spent restocking shelves?  (2 marks)

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\(35\text{%}\)

Show Worked Solution
\(\text{Percentage of day restocking shelves}\) \(=1-(0.42+0.18+0.05)\)
  \(=1-0.65=0.35=35\text{%}\)

 

\(\therefore\ \text{Brittany spent 35% of her day restocking shelves.}\)

Percentages, SM-Bank 010

The breakdown of Joanna's weekly spending is shown in the sector graph below.

What percentage of Joanna's weekly spending was on entertainment?  (2 marks)

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\(10\text{%}\)

Show Worked Solution
\(\text{Percentage spent on Entertainment}\) \(=100-(20+40+10+20)\)
  \(=10\text{%}\)

 
\(\therefore\ \text{Joanna spent } 10\text{% on Entertainment.}\)

Percentages, SM-Bank 009

Convert the following decimals to percentages.

  1. 0.83  (1 mark)

  2. 0.7  (1 mark)

  3. 0.03  (1 mark)

  4. 1.45  (1 marks)

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a.     \(83\%\)

b.     \(70\%\)

c.     \(3\%\)

d.     \(145\%\)

Show Worked Solution
a.    \(0.83\) \(=0.83\times 100=83\%\)

 

b.     \(0.7\) \(=0.7\times 100=70\%\)

 

c.    \(0.03\) \(=0.03\times 100=3\%\)

 

d.     \(1.45\) \(=1.45\times 100=145\%\)

Percentages, SM-Bank 008

Convert the following percentages to fractions in simplest form.

  1. 89%  (1 mark)

  2. 55%  (1 mark)

  3. 164%  (2 mark)

  4. 385%  (2 marks)

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a.     \(\dfrac{89}{100}\)

b.     \(\dfrac{11}{20}\)

c.     \(1\ \dfrac{16}{25}\)

d.     \(3\ \dfrac{17}{20}\)

Show Worked Solution
a.    \(89\%\) \(=\dfrac{89}{100}\)

 

b.     \(55\%\) \(=\dfrac{55}{100}=\dfrac{11}{20}\)

 

c.    \(164\%\) \(=\dfrac{164}{100}=1\dfrac{64}{100}=1\dfrac{16}{25}\)

 

d.     \(385\%\) \(=\dfrac{385}{100}=3 \dfrac{85}{100}=3\ \dfrac{17}{20}\)