smc-4609-35-Best buys

Rates, SM-Bank 092 MC

Jenny needs to reduce her discretionary spending which is shown in the table below.

Spend	Amount	How Often
Gym membership	$50	Monthly
Air travel	$120	Quarterly
KFC lunch	$14	2 days per week
Football tickets for 26 rounds	$25	Weekly

Which action will save her the most?

Cancel gym membership.
Stop air travel.
Reduce KFC to once per week.
Stop going to football games.

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$D$

Show Worked Solution

$\text{Calculate the yearly saving of each action}$

$\text{Gym membership}=$50\times 12 =$600$

$\text{Air travel}=$120\times 4=$480$

$\text{KFC lunch}=\bigg(\dfrac{14\times 52}{2}\bigg)=$364$

$\text{Football tickets}=26\times 25=$650$

$\text{Penrith Panthers tickets costs the most each year}$
$\text{so she should stop going to Penrith games.}$

$\Rightarrow D$

Rates, SM-Bank 091 MC

Rhonda needs to reduce her discretionary spending which is shown in the table below.

Spend	Amount	How Often
Car Wash	$80	Monthly
Hairdresser	$150	Quarterly
Thai take-away	$15	2 nights per week
Streaming services	$12	Weekly

Which action will save her the most?

Stop washing the car.
Stop going to the hairdresser.
Reduce Thai take-away to once per week.
Cancel streaming services.

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$A$

Show Worked Solution

$\text{Calculate the yearly saving of each action}$

$\text{Car wash}=$80\times 12 =$960$

$\text{Hairdresser}=$150\times 4=$600$

$\text{Thai}=15\times 52=$780$

$\text{Streaming services}=12\times 52=$624$

$\text{Washing the car costs the most each year}$
$\text{so she should stop washing the car.}$

$\Rightarrow A$

Rates, SM-Bank 069

An oyster farm sells bags of oysters in four different sizes.

Bag Size	1 kg	2 kg	3 kg	5 kg
Price	$12.00	$23.10	$37.00	$55.00

What is the lowest price a customer can pay for 7 kg of oysters, given that you must buy whole bags? (2 marks)

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$$78.10$

Show Worked Solution

$\text{Calculate the cost per litre for each size:}$

$1\ \text{L}$	$=$12.00\text{/kg}$
$2\ \text{L}$	$= \dfrac{23.10}{2} =$11.55\text{/kg}$
$3\ \text{L}$	$=\dfrac{37.00}{3} \approx $12.33\text{/kg}$
$5\ \text{L}$	$=\dfrac{55.00}{5}= $11.00\text{/kg}$

$\therefore\ \text{Cheapest price to buy 7 kg}$

$=1\times 55.00+1\times 23.10$

$=$78.10$

Rates, SM-Bank 068

A farmers' market sells olive oil in four different sizes.

Size	0.5 litre	1 litre	1.5 litres	3 litres
Price	$3.75	$7.90	$11.70	$24.00

What is the lowest price a customer can pay for 6 litres of olive oil? (2 marks)

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$$45.00$

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$\text{Calculate the cost per litre for each size:}$

$0.5\ \text{L}$	$=$3.75\times 2=$7.50\text{/L}$
$1\ \text{L}$	$= $7.90\text{/L}$
$1.5\ \text{L}$	$=\dfrac{11.70}{1.5} = $7.80\text{/L}$
$3\ \text{L}$	$=\dfrac{24.00}{3}= $8.00\text{/L}$

$\therefore\ \text{Cheapest price to buy 6 L}$

$=12\times 3.75$

$=$45.00$

Rates, SM-Bank 067

A fish market sells prawns in four different sizes.

Size	0.5 kg	1 kg	2 kg	4 kg
Price	$8.25	$16.30	$34.00	$65.50

What is the lowest price a customer can pay for 6 kg of prawns? (2 marks)

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$$97.80$

Show Worked Solution

$\text{Calculate the cost per kg for each size:}$

$0.5\text{kg}$	$=$8.25\times 2=$16.50\text{/kg}$
$1\text{kg}$	$= $16.30\text{/kg}$
$2\text{kg}$	$=\dfrac{34.00}{2} = $17.00\text{/kg}$
$4\text{kg}$	$=\dfrac{65.50}{4} \approx $16.38\text{/kg}$

$\therefore\ \text{Cheapest price to buy 6 kg}$

$=6\times 16.30$

$=$97.80$

Rates, SM-Bank 066

A farmers' market sells potatoes in four different sizes.

Size	1 kg	2 kg	3 kg	5 kg
Price	$3.40	$6.10	$9.30	$15.75

What is the lowest price a customer can pay for 8 kg of potatoes? (2 marks)

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$$24.40$

Show Worked Solution

$\text{Calculate the cost per kg for each size:}$

$1\text{kg}$	$=$3.40\text{/kg}$
$2\text{kg}$	$=\dfrac{6.10}{2} = $3.05\text{/kg}$
$3\text{kg}$	$=\dfrac{9.30}{3} = $3.10\text{/kg}$
$4\text{kg}$	$=\dfrac{15.75}{5} =$3.15\text{/kg}$

$\therefore\ 2\text{kg packet is the cheapest.}$

$\therefore\ \text{Cheapest price to buy 8 kg}$

$=4\times 6.10$

$=$24.40$

Rates, SM-Bank 059

An avocado farmer sells her avocados in four different sizes.

Size	1 kg	2 kg	3 kg	4 kg
Price	$6.35	$13.00	$19.00	$25.10

What is the lowest price a customer can pay for 8 kg of avocados? (2 marks)

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$$50.20$

Show Worked Solution

$\text{Calculate the cost per kg for each size:}$

$1\text{kg}$	$=$6.35\text{/kg}$
$2\text{kg}$	$=\dfrac{13}{2} = $6.50\text{/kg}$
$3\text{kg}$	$=\dfrac{19}{3} = $6.33\text{/kg}$
$4\text{kg}$	$=\dfrac{25.10}{4} \approx $6.28\text{/kg}$

$\therefore\ 4\text{kg packet is the cheapest.}$

$\therefore \text{Cheapest price to buy 8 kg}$

$=2\times 25.10$

$=$50.20$

Rates, SM-Bank 058 MC

A shop sells four sizes of chocolate bar.

Which packet costs the least per gram?

Packet 1
Packet 2
Packet 3
Packet 4

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$B$

Show Worked Solution

$\text{Packet 1}$	$=\dfrac{288}{200} = 1.44\ \text{c/g}$
$\text{Packet 2}$	$=\dfrac{310}{220} = 1.41\ \text{c/g}$
$\text{Packet 3}$	$=\dfrac{181}{125} = 1.45\ \text{c/g}$
$\text{Packet 4}$	$=\dfrac{497}{350} = 1.42\ \text{c/g}$

$\therefore\ \text{Packet 2 costs the least per gram.}$

$\Rightarrow B$

\(1\ \text{L}\)	\(=$12.00\text{/kg}\)
\(2\ \text{L}\)	\(= \dfrac{23.10}{2} =$11.55\text{/kg}\)
\(3\ \text{L}\)	\(=\dfrac{37.00}{3} \approx $12.33\text{/kg}\)
\(5\ \text{L}\)	\(=\dfrac{55.00}{5}= $11.00\text{/kg}\)

\(0.5\ \text{L}\)	\(=$3.75\times 2=$7.50\text{/L}\)
\(1\ \text{L}\)	\(= $7.90\text{/L}\)
\(1.5\ \text{L}\)	\(=\dfrac{11.70}{1.5} = $7.80\text{/L}\)
\(3\ \text{L}\)	\(=\dfrac{24.00}{3}= $8.00\text{/L}\)

\(0.5\text{kg}\)	\(=$8.25\times 2=$16.50\text{/kg}\)
\(1\text{kg}\)	\(= $16.30\text{/kg}\)
\(2\text{kg}\)	\(=\dfrac{34.00}{2} = $17.00\text{/kg}\)
\(4\text{kg}\)	\(=\dfrac{65.50}{4} \approx $16.38\text{/kg}\)

\(1\text{kg}\)	\(=$3.40\text{/kg}\)
\(2\text{kg}\)	\(=\dfrac{6.10}{2} = $3.05\text{/kg}\)
\(3\text{kg}\)	\(=\dfrac{9.30}{3} = $3.10\text{/kg}\)
\(4\text{kg}\)	\(=\dfrac{15.75}{5} =$3.15\text{/kg}\)

\(1\text{kg}\)	\(=$6.35\text{/kg}\)
\(2\text{kg}\)	\(=\dfrac{13}{2} = $6.50\text{/kg}\)
\(3\text{kg}\)	\(=\dfrac{19}{3} = $6.33\text{/kg}\)
\(4\text{kg}\)	\(=\dfrac{25.10}{4} \approx $6.28\text{/kg}\)

\(\text{Packet 1}\)	\(=\dfrac{288}{200} = 1.44\ \text{c/g}\)
\(\text{Packet 2}\)	\(=\dfrac{310}{220} = 1.41\ \text{c/g}\)
\(\text{Packet 3}\)	\(=\dfrac{181}{125} = 1.45\ \text{c/g}\)
\(\text{Packet 4}\)	\(=\dfrac{497}{350} = 1.42\ \text{c/g}\)