SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Measurement, STD2 M7 2024 HSC 17

The cost of electricity is 30.13 cents per kWh .

Calculate the cost of using a 650 W air conditioner for 6 hours.   (2 marks)

Show Answers Only

\(\text{Cost} =\$ 1.18\)

Show Worked Solution

\(\text{Usage}=6 \times 650=3900\, \text{W}=3.9\, \text{kW}\)

\(\text{Cost} =3.9 \times 30.13=117.507 \,\text{c}=\$ 1.18 \, \text {(nearest cent)}\)

Measurement, STD2 M7 2021 HSC 27

The price and the power consumption of two different brands of television are shown.

The average cost for electricity is 25c/kWh. A particular family watches an average of 3 hours of television per day.

  1. The annual cost of electricity for Television A for this family is $48.18.
  2. For this family, what is the difference in the annual cost of electricity between Television A and Television B?  (2 marks)

  3. For this family, how many years will it take for the total cost of buying and using Television A to be equal to the cost of buying and using Television B?  (2 marks)

Show Answers Only
  1. `$4.38`
  2. `5\ text(years)`
Show Worked Solution
a.   `text{Annual power usage (B)}` `= 160 xx 3 xx 365`
    `=175\ 200`
    `=175.2\ text(kWh)`

♦ Mean mark part (a) 49%.
  `text{Annual cost (B)}` `= 175.2 xx 0.25`
    `=$43.80`

 

  `text{Difference in cost}` `= 48.18 – 43.80`
    `=$4.38`

♦♦ Mean mark part (b) 23%.
b.   `text{Difference in price}` `= 921.90 – 900`
    `=$21.90`

 

  `text(Years to even out cost)` `=21.90/4.38`
    `=5\ text{years}`

Measurement, STD2 M7 SM-Bank 12

Francis is buying a fridge. The energy usage of his two choices are below:

Fridge 1 (5 star rating): 227 kWh per year

Fridge 2 (2 star rating): 492 kWh per year

Each fridge has an expected life of 8 years.

If electricity costs 32.4 cents per kWh, how much will Francis save in electricity over the expected life of the more energy efficient fridge, to the nearest dollar?  (2 marks)

Show Answers Only

`$687`

Show Worked Solution

`text(Energy cost of fridge 1)`

`= 227 xx 0.324 xx 8`

`= $588.38`

`text(Energy cost of fridge 2)`

`= 492 xx 0.324 xx 8`

`= $1275.26`

`:.\ text(Energy saving)` `= 1275.26 – 588.38`
  `= 686.88`
  `= $687`

Measurement, STD2 M7 2018 HSC 28c

Every day, a 1200-watt microwave oven is used for 45 minutes at 40% power. Electricity is charged at $0.25 per kWh.

What is the cost of running this microwave oven for 180 days?  (3 marks)

Show Answers Only

`$16.20`

Show Worked Solution
`text(Daily usage)` `= 1200 xx 45/60 xx 40text(%)`
  `= 360\ text(watts)`

 

`text(180 day usage)` `= 180 xx 360`
  `= 64\ 800\ text(watts)`
  `= 64.8\ text(kW)`

 

`:.\ text(C)text(ost over 180 days)` `= 64.8 xx 0.25`
  `= $16.20`

Measurement, STD2 M7 SM-Bank 1

Bikram runs a hot yoga studio.

If it costs 34 cents for 1-kilowatt (1000 watts) for 1 hour, how much does it cost him to run three 3200-watt heaters from 9:00 am to 12:30 pm on a single day? (Give your answer to the nearest cent)  (2 marks)

Show Answers Only

`$11.42`

Show Worked Solution

`text(Total energy usage)`

`= 3 xx 3200 xx 3.5\ text(hours)`

`= 33\ 600\ text(watts)`

 

`:.\ text(C)text(ost)` `= (33\ 600)/1000 xx 0.34`
  `= 11.424`
  `= $11.42\ \ \ text{(nearest cent)}`

Measurement, STD2 M1 2016 HSC 28b

The cost of buying a new heater is $990. It has an energy consumption of 505 kWh per year.

Energy is charged at the rate of $0.35 kWh.

How much will it cost in total to purchase and then run this heater for five years?  (2 marks)

Show Answers Only

`$1873.75`

Show Worked Solution

`text(C)text(ost to run heater for 5 years)`

`= 5 xx 505 xx 0.35`

`= $883.75`
 

`:.\ text(Total purchase and running cost)`

`= 883.75 + 990`

`= $1873.75`