smc-4462-35-% Increase/Decrease

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 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 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)

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$32\%$

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$\text{Strategy 1}$

$\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)

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$38\%$

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$\text{Strategy 1}$

$\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)

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$10\text{%}$

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$\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 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 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)

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$24.6\ \text{metres}$

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$\text{Method 1}$

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

$\text{Method 2 (Advanced)}$

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

Percentages, SM-Bank 058 MC

The price of computer A is $500 and the price of computer B is 300% more than the price of computer A. What is the price of computer B?

$2000
$1500
$1250
$1000

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$A$

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$\text{Price of Computer B}$	$=500 + 500\times 300\%$
	$=500+500\times 3$
	$=$2000$

$\Rightarrow A$

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)

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$10\text{%}$

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$\text{Total kilograms lost}$

$=2.8+3+2.2=8.0$

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

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)

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$65\text{ minutes}$

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$\text{Solution 1}$

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

$\text{Solution 2 (Advanced)}$

$\text{Time}$

$=50\times 1.3=65\ \text{minutes}$

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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$16.2\text{ kilograms}$

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$\text{Solution 1}$

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

$\text{Solution 2}$

$\text{Weight}$

$=12\times 1.35=16.2\ \text{kilograms}$

Percentages, SM-Bank 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?

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

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$D$

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 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 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 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)

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$78\ \text{laps}$

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$\text{1st session} = 50\ \text{laps}$

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

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

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

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

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

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

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

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

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

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

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