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Ratio, SM-Bank 011

Fully simplify the following ratios.

  1. \(24:18\)  (1 mark)

  2. \(180:81\)  (1 mark)

  3. \(14:49:56\)  (1 mark)

Show Answers Only

a.    \(4:3\) 

b.    \(20:9\)

c.    \(2:7:8\)

Show Worked Solution
a.    \(24 :18\) \(=\dfrac{24}{6}:\dfrac{18}{6}\) \(\ \ \text{(Divide by HCF of 24 and 18.)}\)
    \(=4:3\)  

 

b.    \(180 :81\) \(=\dfrac{180}{9}:\dfrac{81}{9}\) \(\ \ \text{(Divide by HCF of 180 and 81.)}\)
    \(=20:9\)  

 

c.    \(14 :49:56\) \(=\dfrac{14}{7}:\dfrac{49}{7}:\dfrac{56}{7}\) \(\ \ \text{(Divide by HCF of 14, 49 and 56.)}\)
    \(=2:7:8\)  

Ratio, SM-Bank 008

Complete each pair of equivalent ratios.  (3 marks)

a.    
\(16:12=\)
  
 \(:3\)
b.
 \(18:24=\)
  
 \(:4\)
c. \(54:9=\)
  
 \(:1\)
Show Answers Only

a.    \(4:3\)

b.    \(3:4\)

c.    \(6:1\)

Show Worked Solution
a.    \(16 :12\) \(=(16÷4):(12÷4)\)
  \(=4:3\)

 

b.    \(18 :24\) \(=(18÷6):(24÷6)\)
  \(=3:4\)

 

c.    \(54 :9\) \(=(54÷9):(9÷9)\)
  \(=6:1\)

Ratio, SM-Bank 007

Complete each pair of equivalent ratios.  (3 marks)

a.    \(3:4\) \(=9:\)
 
b.    \(2:5\)
 \(=8:\)
  
c.    \(10:3\)
 \(=30:\)
  
Show Answers Only

a.    \(9:12\)

b.    \(8:20\)

c.    \(30:9\)

Show Worked Solution
a.    \(3 :4\) \(=3\times 3:4\times 3\)
  \(=9:12\)

 

b.    \(2 :5\) \(=2\times 4:5\times 4\)
  \(=8:20\)

 

c.    \(10 :3\) \(=10\times 3:3\times 3\)
  \(=30:9\)

Ratio, SM-Bank 006 MC

At the Year 7 camp, there were 20 teachers and 180 students.

What is the ratio of students to the total number of people at the camp?

  1. \(9:2\)
  2. \(180:20\)
  3. \(9:10\)
  4. \(9:1\)
Show Answers Only

\(C\)

Show Worked Solution
\(\text{students}\ :\ \text{total}\) \(=180:(20+180)\)
  \(=180:200\)
  \(=9:10\)

 
\(\Rightarrow C\)

Ratio, SM-Bank 003

James was building a lego house and has the pieces below left over.

Calculate:

  1. the ratio of blue bricks to yellow.  (1 mark)

  2. the ratio of pink bricks to the total leftover bricks.  (1 mark)

  3. the ratio of yellow bricks to other leftover bricks.  (1 mark)

Show Answers Only

a.    \(4:5\)

b.    \(2:11\)

c.    \(5:6\)

Show Worked Solution

a.    \(\text{Blue}:\text{Yellow}=4:5\)

b.    \(\text{Total Bricks}=2+4+5=11\)

\(\text{Pink}:\text{Total}=2:11\)

c.    \(\text{Total other bricks}=2+4=6\)

\(\text{Yellow}:\text{Other}=5:6\)

Ratio, SM-Bank 002

A fruit bowl contains 8 apples, 7 bananas, 1 pear and 13 oranges.

Calculate:

  1. the ratio of apples to oranges.  (1 mark)

  2. the ratio of oranges to the total pieces of fruit in the bowl.  (1 mark)

  3. the ratio of pears to other pieces of fruit.  (1 mark)

Show Answers Only

a.    \(8:13\)

b.    \(13:29\)

c.    \(1:28\)

Show Worked Solution

a.    \(\text{Apples}:\text{Oranges}=8:13\)

b.    \(\text{Total Fruit}=8+7+1+13=29\)

\(\text{Oranges}:\text{Total}=13:29\)

c.    \(\text{Total other fruit}=8+7+13=28\)

\(\text{Pear}:\text{Other}=1:28\)

Ratio, SM-Bank 001

A bag contains 3 red marbles, 4 blue marbles and 8 white marbles.

Calculate:

  1. the ratio of red marbles to blue marbles.  (1 mark)

  2. the ratio of white marbles to the total number of marbles.  (1 mark)

  3. the ratio of blue marbles to other colours.  (1 mark)

Show Answers Only

a.    \(3:4\)

b.    \(8:15\)

c.    \(4:11\)

Show Worked Solution

a.    \(\text{Red}:\text{Blue}=3:4\)

b.    \(\text{Total marbles}=3+4+8=15\)

\(\text{White}:\text{Total}=8:15\)

c.    \(\text{Total other marbles}=3+8=11\)

\(\text{Blue}:\text{Other}=4:11\)

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)

Show Answers Only

\(33\text{%}\)

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

 

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

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)

Show Answers Only

\(85\text{%}\)

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

 

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

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.

  1. Calculate the loss that Iggy made.  (1 mark)

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

Show Answers Only

a.    \($1050\)

b.    \(30\%\)

Show Worked Solution
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 086

Janice bakes cupcakes for the local market. The ingredients she uses in each of the cupcakes cost $1.90.

Last weekend she sold the cupcakes for $3.99 each.

  1. What was Janice's profit per cupcake?  (1 mark)

  2. Calculate Janice's percentage profit per cupcake based on the cost of the ingredients.  (2 marks)

Show Answers Only

a.    \($2.09\ \text{per cupcake}\)

b.    \(110\%\)

Show Worked Solution
a.    \(\text{Profit}\) \(=3.99-1.90\)
  \(=$2.09\)

 

b.    \(\text{Percentage Profit}\) \(= \dfrac{\text{Profit}}{\text{Cost of ingredients}}\times 100\%\)
  \(=\dfrac{2.09}{1.90}\times 100\%\)
  \(=110\%\)

Percentages, SM-Bank 085

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

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

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

Show Answers Only

a.    \($8624\)

b.    \(56\text{%}\)

Show Worked Solution
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 \($21\ 000\).

  1. Calculate the loss that Jeffrey made.  (1 mark)

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

Show Answers Only

a.    \($14\ 000\)

b.    \(40\%\)

Show Worked Solution

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 083

Jock is a real estate agent who is paid 2.5% commission on all house sales.

Last month he sold houses to the value of \($2.5\ \text{million}\).

How much pay did Jock receive in the form of commission last month?  (2 marks)

Show Answers Only

\($62\ 500\)

Show Worked Solution
\(\text{Commission}\) \(= 2.5\text{%}\times 2\ 500\ 000\)
  \(=\dfrac{25}{1000}\times 2\ 500\ 000\)
  \(=$62\ 500\)

  
\(\therefore\ \text{Jock earned }$62\ 500\ \text{in commission.}\)

Percentages, SM-Bank 082

Louella is a boat broker who is paid 6.5% commission on all boat sales.

Last quarter she sold boats to the value of \($443\ 000\).

How much pay did Louella receive in the form of commission last quarter?  (2 marks)

Show Answers Only

\($28\ 795\)

Show Worked Solution
\(\text{Commission}\) \(= 6.5\text{%}\times 443\ 000\)
  \(=\dfrac{65}{1000}\times 443\ 000\)
  \(=$28\ 795\)

  
\(\therefore\ \text{Louella earned }$28\ 795\ \text{in commission.}\)

Percentages, SM-Bank 081

Hendry is a salesperson who is paid 5% commission on all sales.

Last month he sold goods to the value of  \($45\ 300\).

How much commission did Hendry receive last month?  (2 marks)

Show Answers Only

\($2265\)

Show Worked Solution
\(\text{Commission}\) \(= 5\%\times 45\ 300=\dfrac{5}{100}\times 45\ 300\)
  \(=$2265\)

  
\(\therefore\ \text{Hendry earned }$2265\ \text{in commission.}\)

Percentages, SM-Bank 080

The sale price of a parrot is $400.

The pet store gives Albert 25% off the sale price.

Albert has a pet store discount voucher that gives him a further $60 off the sale price.

What percentage of the original price does Albert pay for the parrot?  (2 marks)

Show Answers Only

\(60\text{%}\)

Show Worked Solution
\(\text{Sale Price}\) \(= \$400-(25\text{%}\times 400)\)
  \(=400-100\)
  \(=$300\)

  
\(\text{Purchase price}=300-60=$240\)

\(\text{Percentage of original price}\) \(=\dfrac{240}{400}\times 100\)
  \(=\dfrac{6}{10}\times 100\)
  \(=60\text{%}\)

Percentages, SM-Bank 079

A family ticket to Taronga Zoo in Sydney reduced in price from $90 to $73.80.

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

Show Answers Only

\(18\text{%}\)

Show Worked Solution

\(\text{Price decrease}=90-73.80=$16.20\)

\(\text{Percentage decrease}\) \(= \dfrac{16.2}{90}\times 100\)
  \(=0.18\times 100\)
  \(=18\text{%}\)

 

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)

Show Answers Only

\(25\text{%}\)

Show Worked Solution

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

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

 

Percentages, SM-Bank 077

A loaf of bread is on sale with a 15% discount.

In the last hour of trading, the bread is reduced a further 20% on the already discounted price.

What is the overall percentage discount on the bread?  (2 marks)

Show Answers Only

\(32\%\)

Show Worked Solution

\(\text{Strategy 1}\)

\(\text{Assume the bread costs }$1.00.\)

\(\text{Cost after }15\text{% discount}=$0.85\)

\(\text{Cost after further }20\text{% discount}\) \(= 0.85-(20\%\times 0.85)\)
  \(=0.85-0.17\)
  \(=$0.68\)

 
\(\therefore\ \text{Overall discount} =(1.00-0.68)\times 100 =32\text{%}\)
 

\(\text{Strategy 2}\)

\(\text{Overall discount}\) \(=1-(1\times 0.85\times 0.80)\)
  \(=1.00-0.68\)
  \(=0.32\)
  \(=32\%\)

Percentages, SM-Bank 076

A farmer sells a box of oranges to a supermarket with a 15% markup.

The supermarket then adds a further 20% on the already increased price.

What is the overall percentage markup on the box of oranges?  (2 marks)

Show Answers Only

\(38\%\)

Show Worked Solution

\(\text{Strategy 1}\)

\(\text{Assume the box of oranges costs }$1.00.\)

\(\text{Cost after }15\text{% markup}=$1.15\)

\(\text{Cost after further }20\text{% increase}\) \(= 1.15+(20\%\times 1.15)\)
  \(=1.15+0.23=$1.38\)

 
\(\therefore\ \text{Overall markup} =(1.38-1.00)\times 100 =38\%\)
 

\(\text{Strategy 2}\)

\(\text{Overall markup}\) \(=(1\times 1.15\times 1.20)-1\)
  \(=1.38-1.00=0.38=38\%\)

Percentages, SM-Bank 075

A car dealer decreases the price of a car from $50 000 to $45 000.

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

Show Answers Only

\(10\text{%}\)

Show Worked Solution

\(\text{Price decrease}= 50\ 000-45\ 000=$5\ 000\)

\(\therefore\ \text{Percentage Decrease}\) \(= \dfrac{5\ 000}{50\ 000}\times 100\)
  \(=0.10\times 100\)
  \(= 10\text{%}\)

Percentages, SM-Bank 074

Lucia is saving her money to buy a jet ski.

After 3 months, she had saved 40% of the cost of the jet ski.

After 5 months, she had saved another $1200 and now had 60% of the cost of the jet ski.

How much does the jet ski cost?  (2 marks)

Show Answers Only

\($6000\)

Show Worked Solution
\(60\%-40\%\) \(= $1200\)
\(\therefore 20\%\) \(= $1200\)
\(\therefore\ 1\%\) \(= $60\)

 

\(\therefore\ \text{The cost of the jet ski}\) \(= 100\times 60= $6000\)

Percentages, SM-Bank 071

Lancelot bought a new round table for $2810.50 inclusive of 10% GST.

What was the price of the round table before the GST was added?  (2 marks)

Show Answers Only

\($2555\)

Show Worked Solution

\(\text{Round table has had 10% added to the price.}\)

\(\therefore\ $2810.50\ \text{represents}\ 110\text{%}\ \text{of the original price}\)

\(\therefore\ \dfrac{110}{100}\ \times\ \text{Original price}\) \(=$2810.50\)
\(\therefore\ \text{Original price}\) \(=\dfrac{$2810.50\times 10}{11}\)
  \(=$2555\)

Percentages, SM-Bank 070

Mickey bought a plane ticket to London for $1716 inclusive of 10% GST.

What was the price of the ticket before the GST was added?  (2 marks)

Show Answers Only

\($1560\)

Show Worked Solution

\(\text{Plane ticket has had 10% added to the price.}\)

\(\therefore\ $1716\ \text{represents}\ 110\text{%}\ \text{of the original price}\)

\(\therefore\ \dfrac{110}{100}\ \times\ \text{Original price}\) \(=$1716\)
\(\therefore\ \text{Original price}\) \(=\dfrac{$1716\times 10}{11}\)
  \(=$1560\)

Percentages, SM-Bank 069

James purchased a pair of football boots for $358.05.

This price included 10% GST.

What was the price of the shoes before the GST was added?  (2 marks)

Show Answers Only

\($325.50\)

Show Worked Solution

\(\text{Football boots have had 10% added to the price.}\)

\(\therefore\ $358.05\ \text{represents}\ 110\text{%}\ \text{of the original price}\)

\(\therefore\ \dfrac{110}{100}\ \times\ \text{Original price}\) \(=$358.05\)
\(\therefore\ \text{Original price}\) \(=\dfrac{358.05\times 10}{11}\)
  \(=$325.50\)

Percentages, SM-Bank 068

Minerva purchased a book online and a discount of 35% was applied at checkout.

If Minerva paid $29.90 with the discount, what was the original price of the book.  (2 marks)

Show Answers Only

\($46\)

Show Worked Solution

\(\text{Book price discounted by 35%.}\)

\(\therefore\ $29.90\ \text{represents}\ \dfrac{65}{100}\ \text{of the original price}\)

\(\therefore\ \dfrac{65}{100}\ \times\ \text{Original price}\) \(=$29.90\)
\(\therefore\ \text{Original price}\) \(=\dfrac{29.90\times 100}{65}=$46\)

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)

Show Answers Only

\(16.2\text{ kilograms}\)

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. \(-7\ ,\ -6\ ,\ \dfrac{5}{3}\ ,\ 80\text{%}\)
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\(B\)

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. \(-2\ ,\ -3\ ,\ \dfrac{5}{4}\ ,\ 25\text{%}\)
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\(A\)

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)

 

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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)

 

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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)

 

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\(74\text{%}\)

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