smc-4462-20-% of a quantity

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.

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

--- 1 WORK AREA LINES (style=lined) ---
Calculate Janice's percentage profit per cupcake based on the cost of the ingredients. (2 marks)

--- 2 WORK AREA LINES (style=lined) ---

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 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 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)

--- 4 WORK AREA LINES (style=lined) ---

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)

--- 5 WORK AREA LINES (style=lined) ---

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 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?

$2\ 773\ 100$
$2\ 710\ 500$
$2\ 147\ 600$
$2\ 091\ 300$

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 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)

--- 4 WORK AREA LINES (style=lined) ---

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 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)

--- 5 WORK AREA LINES (style=lined) ---

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)

--- 3 WORK AREA LINES (style=lined) ---

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 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)

--- 4 WORK AREA LINES (style=lined) ---

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 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)

--- 3 WORK AREA LINES (style=lined) ---

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 021

A sport store has a sale.

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

--- 5 WORK AREA LINES (style=lined) ---

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)

--- 5 WORK AREA LINES (style=lined) ---

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 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?

Show Answers Only

$B$

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 013

Find:

2% of $14.50. (2 mark)

--- 2 WORK AREA LINES (style=lined) ---
15% of 300 kg. (2 marks)

--- 3 WORK AREA LINES (style=lined) ---
$12\dfrac{1}{2}\%$ of 880 km. (2 marks)

--- 3 WORK AREA LINES (style=lined) ---

Show Answers Only

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:

10% of $325. (1 mark)

--- 2 WORK AREA LINES (style=lined) ---
30% of 1200 kg. (2 marks)

--- 2 WORK AREA LINES (style=lined) ---
75% of 500 km. (2 marks)

--- 2 WORK AREA LINES (style=lined) ---

Show Answers Only

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

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

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

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

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

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

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

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

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

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