smc-4462-45-% Discount

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 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)

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$60\text{%}$

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

$\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)

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$18\text{%}$

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$\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 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)

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$$46$

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$\text{Book price discounted by 35%.}$

$\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)

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$400\ 000\ \text{litres}$

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$\text{Capacity has decreased by 30%.}$

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

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

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)

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$$240$

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

$\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 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?

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$A$

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

$\text{A}$	$= 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 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)

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$$224$

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$\text{Method 1}$

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

$\text{Method 2 (Advanced)}$

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

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)

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$$180$

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$\text{Method 1}$

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

$\text{Method 2 (Advanced)}$

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

Percentages, SM-Bank 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)

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$$24$

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$\text{Value of the discount}$

$10\text{% of }160 = 16$

$\therefore\ 5\text{% of }160=8$

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

$\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.

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$C$

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$\text{C}\text{ost of each option:}$

$\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 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)

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$$285$

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$\text{Solution 1}$

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

$\text{Solution 2 (Advanced)}$

$\text{Price of mobile}$

$=0.75\times 380=$285$

Percentages, SM-Bank 028

A hockey stick is on sale, reduced from $220 to $165.

What percentage discount has been applied? (2 marks)

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$25\text{%}$

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$\text{Discount}$	$=\dfrac{\text{reduction}}{\text{original price}}\times 100$
	$=\dfrac{220-165}{220}\times 100$
	$=25\text{%}$

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)

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$$2\ 241\ 000$

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$\text{Solution 1}$

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

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

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$$17.55$

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$10\text{% discount}$

$=\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)

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$$18$

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$\text{Solution 1}$

$\text{Sale price}$

$= 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 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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$B$

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

$\text{A}$	$= 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 006 MC

Zane bought a soccer ball that was on sale at 50% discount.

He paid $19.95 for the soccer ball.

Which amount below is the best estimate of the original price of the soccer ball?

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$A$

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$19.95\approx $20\ $ and $\ 50\text{%}=\dfrac{1}{2}$

$\therefore\ \dfrac{1}{2}\ \times\ \text{Original Price}$	$\approx $20$
$\therefore\ \text{Original Price}$	$\approx 2\times 20$
	$\approx $40$

$\Rightarrow A$

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

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

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

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

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

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

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

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

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