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Algebra, STD2 EQ-Bank 27

Dial-A-Lift Luxury Transport offers ride services in the local area of Maitland.

They currently use the formula below to calculate the cost of each fare.

   Total fare \(=\) Booking fee \(+\) Cost per kilometre \(\times\) Number of kilometres travelled

A spreadsheet used to calculate the total fare is shown.
 

  1. By using appropriate grid references, write down a formula that could have been used in cell E4.   (2 marks)

  2. A trip with a different number of kilometres travelled is entered, but the booking fee and cost per kilometre remain unchanged. As a result, the value in cell E4 changes to $47.50.
  3. Calculate the value entered in cell B6.   (2 marks)

Show Answers Only

a.    \(=\text{B4}+ \text{B5} \ ^* \ \text{B6}\)

b.    \(\text{Cell B6 value = 13.}\)

Show Worked Solution

a.    \(=\text{B4}+ \text{B5} \ ^* \ \text{B6}\)
 

b.     \(47.5\) \(=15+2.5 n\)
  \(32.5\) \(=2.5n\)
  \(n\) \(=\dfrac{32.5}{2.5}=13\)

 
\(\text{Cell B6 value = 13.}\)

Algebra, STD2 A2 2021 HSC 18

The fuel consumption for a car is 6.7 litres/100 km. On a road trip, the car travels a distance of 1560 km and the fuel cost is $1.45 per litre.

What is the total fuel cost for the trip?   (2 marks)

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`$151.55`

Show Worked Solution

`text(Total fuel used)=6.7 xx 1560/100=104.52\ text(L)`

`text(Total fuel cost)=104.52 xx 1.45=$151.55`

Algebra, STD2 A2 EQ-Bank 3 MC

A car travels 350 km on 40 L of petrol.

What is its fuel consumption?

  1. 7.8 L/100 km
  2. 8.4 L/100 km
  3. 8.8 L/100 km
  4. 11.4 L/100 km
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`D`

Show Worked Solution

`text(40 litres are used to travel  3.5 × 100 km.)`

`text{Fuel consumption (L/100 km)}`

`= 40/3.5 = 11.428 = 11.4\ text(L/100 km)`

`=> D`

Algebra, STD2 A2 2018 HSC 5 MC

The driving distance from Alex's home to his work is 20 km. He drives to and from work five times each week. His car uses fuel at the rate of 8 L/100 km.

How much fuel does he use driving to and from work each week?

  1. 16 L
  2. 20 L
  3. 25 L
  4. 40 L
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`A`

Show Worked Solution

`text(Total distance travelled each week)`

`= 5 xx 2 xx 20= 200\ text(km)` 

`:.\ text(Total fuel used)`

`= 200/100 xx 8\ text(L)= 16\ text(L)`

`=>A`

Algebra, STD2 A2 2017 HSC 14 MC

Kate is comparing two different models of car. Car A uses fuel at the rate of 9 L/100 km. Car B uses 3.5 L/100 km.

Suppose Kate plans on driving 8000 km in the next year.

How much less fuel will she use driving car B instead of car A?

  1. 280 L
  2. 440 L
  3. 720 L
  4. 1000 L
Show Answers Only

`B`

Show Worked Solution

`text(Fuel car)\ A= 8000/100 xx 9= 720\ text(L)`

`text(Fuel car)\ B= 8000/100 xx 3.5= 280\ text(L)`

`:.\ text(Fuel saved car)\ B= 720-280= 440\ text(L)`

`=>B`

Algebra, STD2 A2 2016 HSC 26c

Peta’s car uses fuel at the rate of 5.9 L /100 km for country driving and 7.3 L /100 km for city driving. On a trip, she drives 170 km in the country and 25 km in the city.

Calculate the amount of fuel she used on this trip.   (2 marks)

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`11.855\ text(L)`

Show Worked Solution

`text(Fuel used in country)= 170 xx 5.9/100= 10.03\ text(L)`

`text(Fuel used in city)= 25 xx 7.3/100= 1.825\ text(L)`

`:.\ text(Total fuel used)= 10.03 + 1.825= 11.855\ text(L)`

Algebra, STD2 A2 2014 HSC 27b

Xuso is comparing the costs of two different ways of travelling to university.

Xuso’s motorcycle uses one litre of fuel for every 17 km travelled. The cost of fuel is $1.67/L and the distance from her home to the university car park is 34 km. The cost of travelling by bus is  $36.40 for 10 single trips.

Which way of travelling is cheaper and by how much? Support your answer with calculations.   (2 marks)

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`text(Motorcycle is $0.30 cheaper per 1-way trip)`

Show Worked Solution

`text(Compare cost of a 1-way trip)`

`text(Motorcycle)`

`text(Fuel used) = 34/17 = 2\ text(L)`

`text(C)text(ost) = 2 xx $1.67 = $3.34`

`text(Bus)`

`text(C)text(ost) = 36.40/10 = $3.64`

`text(Difference) = $3.64\-3.34\ = $0.30`

 

`:.\ text(Motorcycle is $0.30 cheaper per 1-way trip.)`

Algebra, STD2 A2 2014 HSC 22 MC

Heather’s car uses fuel at the rate of 6.6 L per 100 km for long-distance driving and  8.9 L per 100 km for short-distance driving.

She used the car to make a journey of 560 km, which included 65 km of short-distance driving.  

Approximately how much fuel did Heather’s car use on the journey?

  1. 37 L
  2. 38 L
  3. 48 L
  4. 50 L
Show Answers Only

`B`

Show Worked Solution

`text(Fuel used in short distance)`

`= 65/100 xx 8.9\ text(L) = 5.785\ text(L)`

`text(Fuel used in long distance)`

`= 495/100 xx 6.6\ text(L) = 32.67\ text(L)`

`:.\ text(Total Fuel)= 38.455\ text(L)`  

`=>  B`