smc-4609-40-Unitary method rates

Rates, SM-Bank 096

Mika is making lemonade.

The recipe says she needs 1 cup of sugar for every 3 lemons.

If 7 lemons are used, how many cups of sugar are needed? (2 marks)

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$2\dfrac{1}{3}\ \text{cups}$

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$\text{3 lemons}\rightarrow 1\ \text{cup of sugar}$

$\text{1 lemon}\rightarrow\dfrac{1}{3}\ \text{cup of sugar}$

$\therefore\ 7\ \text{lemons}$	$=7\times\dfrac{1}{3}$
	$=\dfrac{7}{3}$
	$=2\dfrac{1}{3}\ \text{cups}$

Rates, SM-Bank 055

Jesse sells, an average of 150 roller-coaster tickets every 10 minutes. How long will it take him sell 600 tickets? (2 marks)

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$40\ \text{minutes}$

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$10\ \text{minutes}/150\ \text{tickets}$	$=\dfrac{10}{150}\ \text{minutes}/\dfrac{150}{150}\ \text{tickets}$
	$=\dfrac{1}{15}\ \text{minute}/1\ \text{ticket}$
	$=\bigg(\dfrac{1}{15}\times 600\bigg)\ \text{minutes}/600\ \text{tickets}$
	$=40\ \text{minutes}/600\ \text{tickets}$

$\therefore\ \text{It would take}\ 40\ \text{minutes to sell}\ 600\ \text{tickets.}$

Rates, SM-Bank 034

Aurora works part time in a donut shop.

On weekends, she earns 2.5 times as much per hour as she earns on weekdays.

One week, she works 14.5 hours on weekdays and 3 hours on the weekend.

Her pay for the week was $319.

How much does she earn in 1 hour on a weekday? (2 marks)

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$$12.50/\text{hour}$

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$\text{Pay hours}$	$= 14.5+3\times 2.5$
	$=22$

$\text{Earnings for 1 hour}$	$=\dfrac{319}{22}$
	$=$14.50$

$\therefore \text{Aurora earns}\ $14.50\ \text{in 1 hour.}$

Rates, SM-Bank 033

Fleur works part time in a flower shop.

On weekends, she earns 2 times as much per hour as she earns on weekdays.

One week, she works 23 hours on weekdays and 1.5 hours on the weekend.

Her pay for the week was $351.

How much does she earn in 1 hour on a weekday? (2 marks)

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$$13.50/\text{hour}$

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$\text{Pay hours}$	$= 23+2\times 1.5$
	$=26$

$\text{Earnings for 1 hour}$	$=\dfrac{351}{26}$
	$=$13.50$

$\therefore \text{Fleur earns}\ $13.50\ \text{in 1 hour.}$

Rates, SM-Bank 032

Fanny works part time at Guzman y Gomez.

On weekends, she earns 1.5 times as much per hour as she earns on weekdays.

One week, she works 12 hours on weekdays and 8 hours on the weekend.

Her pay for the week was $414.

How much does she earn in 1 hour on a weekday? (2 marks)

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$$17.25/\text{hour}$

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$\text{Pay hours}$	$= 12+ 8 \times 1.5$
	$=24$

$\text{Earnings for 1 hour}$	$=\dfrac{414}{24}$
	$=$17.25$

Rates, SM-Bank 031

Clay has a casual job at the local movie cinema.

On weekends, he earns 1.5 times as much per hour as he earns on weekdays.

One week, he works 20 hours on weekdays and 6 hours on the weekend.

His pay for the week was $498.80.

How much does he earn in 1 hour on a weekday? (2 marks)

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$$17.20/\text{hour}$

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$\text{Pay hours}$	$= 20+6\times 1.5$
	$=29$

$\text{Earnings for 1 hour}$	$=\dfrac{498.80}{29}$
	$=$17.20$

$\therefore \text{Clay earns}\ $17.20\ \text{in 1 hour.}$

Rates, SM-Bank 030

Betty works part time in a clothing shop.

On weekends, she earns 2 times as much per hour as she earns on weekdays.

One week, she works 15 hours on weekdays and 3 hours on the weekend.

Her pay for the week was $367.50.

How much does she earn in 1 hour on a weekday? (2 marks)

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$$17.50/\text{hour}$

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$\text{Pay hours}$	$= 15+3\times 2$
	$=21$

$\text{Earnings for 1 hour}$	$=\dfrac{367.50}{21}$
	$=$17.50$

$\therefore \text{Betty earns}\ $17.50\ \text{in 1 hour.}$

Rates, SM-Bank 029

Brin works part time in a coffee shop.

On weekends, he earns 1.5 times as much per hour as he earns on weekdays.

One week, he works 9 hours on a weekday and 4 hours on the weekend.

His pay for the week was $270.

How much does he earn in 1 hour on a weekday? (2 marks)

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$$18/\text{hour}$

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$\text{Pay hours}$	$= 9+4\times 1.5$
	$=15$

$\text{Earnings for 1 hour}$	$=\dfrac{270}{15}$
	$=$18$

$\therefore \text{Brin earns}\ $18\ \text{in 1 hour.}$

Rates, SM-Bank 024

Gary used 4 litres of paint to paint a wall.

The wall was a rectangle 2 metres high and 3 metres wide.

How many litres of paint would he need to paint a rectangular wall which is 3 metres high and 5 metres wide? (2 marks)

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$10$

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$\text{Area of smaller wall}$

$= 2\times 3$

$= 6\ \text{m}^2$

$\text{S}\text{ince 4 litres of paint are needed to}$

$\text{paint the small wall:}$

$\rightarrow\ \text{Paint needed for 1 m}^2$

$= \dfrac{4}{6}$

$= \dfrac{2}{3}\ \text{litre}$

$\rightarrow\ \text{Area of larger wall}$

$= 3\times 5$

$= 15\ \text{m}^2$

$\text{Paint needed}$	$= 15\times \dfrac{2}{3}$
	$= 10\ \text{litres}$

Rates, SM-Bank 019

It takes Kate 15 seconds to place a brochure in an envelope and seal it.

How many minutes will it take her to pack and seal 42 envelopes? (2 marks)

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$10.5\ \text{minutes}$

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$\text{Time}$	$=42\times 15$
	$=630\ \text{seconds}$
	$=\dfrac{630}{60}\ \text{minutes}$
	$=10.5\ \text{minutes}$

Rates, SM-Bank 017

Constance used 300 grams of sugar to make 12 brownies.

How many grams of sugar will she need to make 18 brownies? (2 marks)

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$450\ \text{grams}$

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$\text{Method 1}$

$\text{Sugar to make 18 brownies}$

$=\dfrac{18}{12}\times 300$

$=1.5\times 300$

$=450\ \text{grams}$

$\text{Method 2 – Unitary Method}$

$300\ \text{g/}12\ \text{cookies}$	$=\dfrac{300}{12}\ \text{g/cookie}$
	$=25\ \text{g/cookie}$

$\text{Sugar to make 18 brownies}$	$=25\times 18$
	$=450\ \text{grams}$

Rates, SM-Bank 014

A brewery can make 1250 cans of ale and 900 cans of lager per hour.

The brewery runs non-stop and each can weighs 350 grams.

How many kilograms of ale and lager, altogether, does the brewery make in 1 full day? (2 marks)

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$18\ 060\ \text{kilograms per day}$

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$\text{Total cans made per hour}$

$=1250+900$

$= 2150$

$\text{Kilograms made in 1 hour}$

$=2150\times 350$

$=752\ 500\ \text{grams}$

$= 752.5\ \text{kilograms}$

$\therefore\ \text{Kilograms made in 1 day}$	$=752.5\times 24$
	$=18\ 060$

Rates, SM-Bank 011 MC

In a science experiment, Albert needs to add 60 millilitres of acid to every 2 litres of water.

If Albert only has 0.5 litres of water left, how many millilitres of acid should he add?

0.15 mL
0.6 mL
15 mL
30 mL

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$C$

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$\text{Given}\ \ 60\ \text{mL}$	$\rightarrow 2\ \text{litres}$
$30\ \text{mL}$	$\rightarrow 1\ \text{litre}$
$\therefore 15\ \text{mL}$	$\rightarrow 0.5\ \text{litres}$

$\therefore 15\ \text{millilitres of acid should be added}$

$\Rightarrow C$

Rates, SM-Bank 010 MC

A tram at the zoo does a complete 5 kilometre loop in 30 minutes.

If the tram travelled at the same speed, how long did it take to complete 2 kilometres?

8 minutes
12 minutes
18 minutes
24 minutes

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$B$

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$30\ \text{minutes}/5\ \text{kms}$	$=\dfrac{30}{5}\ \text{minutes}/\dfrac{5}{5}\ \text{km}$
	$=6\ \text{minutes}/\text{km}$

$\therefore\ \text{Time for 2 kms}$	$=6\times 2$
	$=12\ \text{minutes}$

$\Rightarrow B$

Rates, SM-Bank 009 MC

Sid is selling bike tyre tubes at a market stall.

He makes $54 from selling 6 bike tyre tubes.

All bike tyre tubes cost the same.

How much will Sid make if he sells 11 bike tyre tubes?

$65
$83
$99
$108

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$C$

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$$54/6\ \text{tubes}$	$=\dfrac{$54}{6}/\dfrac{6}{6}\text{tubes}$
	$=$9/\text{tube}$

$\therefore\ \text{Price of 11 tubes}$	$=11\times 9$
	$=$99$

$\Rightarrow C$

Rates, SM-Bank 008

Bryce organises parking for major events in the city.

He has open air parking spaces for 3 cars on every 27 square metres of land.

How many cars could Bryce park on 4680 square metres? (2 marks)

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$520$

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$\text{3 cars/}\ 27\ \text{m}^2=1\ \text{car/}9\ \text{m}^2$

$\therefore\ \text{cars on }4680\ \text{m}^2$	$=\dfrac{4680}{9}$
	$=520\ \text{cars}$

Rates, SM-Bank 007

A young echidna weighed 1200 grams at the beginning of November just before leaving the burrow.

At the end of March it weighed 1850 grams.

Calculate the average rate of growth of the echidna for the 5 month period. (2 marks)

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$130\ \text{g}/ \text{month}$

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$\text{Growth}$	$=1200-1850$
	$=650\ \text{g}$

$\text{Rate of growth}/\text{month}$	$=\dfrac{650}{5}\ \text{g}/\text{month}$
	$=130\ \text{g}/\text{month}$

\(\therefore\ 7\ \text{lemons}\)	\(=7\times\dfrac{1}{3}\)
	\(=\dfrac{7}{3}\)
	\(=2\dfrac{1}{3}\ \text{cups}\)

\(10\ \text{minutes}/150\ \text{tickets}\)	\(=\dfrac{10}{150}\ \text{minutes}/\dfrac{150}{150}\ \text{tickets}\)
	\(=\dfrac{1}{15}\ \text{minute}/1\ \text{ticket}\)
	\(=\bigg(\dfrac{1}{15}\times 600\bigg)\ \text{minutes}/600\ \text{tickets}\)
	\(=40\ \text{minutes}/600\ \text{tickets}\)

\(\text{Time}\)	\(=42\times 15\)
	\(=630\ \text{seconds}\)
	\(=\dfrac{630}{60}\ \text{minutes}\)
	\(=10.5\ \text{minutes}\)

\(\text{Given}\ \ 60\ \text{mL}\)	\(\rightarrow 2\ \text{litres}\)
\(30\ \text{mL}\)	\(\rightarrow 1\ \text{litre}\)
\(\therefore 15\ \text{mL}\)	\(\rightarrow 0.5\ \text{litres}\)

\(\text{Pay hours}\)	\(= 14.5+3\times 2.5\)
	\(=22\)

\(\text{Earnings for 1 hour}\)	\(=\dfrac{319}{22}\)
	\(=$14.50\)

\(\text{Pay hours}\)	\(= 23+2\times 1.5\)
	\(=26\)

\(\text{Earnings for 1 hour}\)	\(=\dfrac{351}{26}\)
	\(=$13.50\)