Utilities and bills questions with answers

Questions

1. Question 1Electricity: meter readings × rate

   The table shows a household's electricity meter readings for a month and the rate charged. Find the cost of the electricity used, in dollars.

   Previous meter reading	Current meter reading	Rate
   30872 kWh	31152 kWh	30 cents per kWh

   Show the worked solution

   1. Step 1: Units used = current reading − previous reading$31152 - 30872 = 280 \text{ kWh}$
   2. Step 2: Cost in cents = units used × rate$280 \times 30 = 8400 \text{ cents}$
   3. Step 3: Change cents to dollars (÷ 100)$\dfrac{8400}{100} = 84$The electricity costs $84.
2. Question 2Water charged in two tiers

   A household uses 52 m³ of water in a month. The table shows the water charges. Find the cost of the water used.

   Water used in a month	Price
   First 40 m³	$1.43 per m³
   Above 40 m³	$1.89 per m³

   Show the worked solution

   1. Step 1: The first tier at the lower rate (in dollars)$40 \times 1.43 = 57.20$
   2. Step 2: The rest at the higher rate$52 - 40 = 12 \text{ m}^3$$12 \times 1.89 = 22.68$
   3. Step 3: Add the two charges$57.20 + 22.68 = 79.88$The water costs $79.88.
3. Question 3A phone bill with extra minutes

   Hui Min's mobile phone plan is shown in the table. In March, Hui Min made 400 minutes of calls. Find the amount of Hui Min's bill for March.

   Monthly fee	Free talk time	Extra calls
   $18	200 min	8 cents per min

   Show the worked solution

   1. Step 1: Extra minutes = minutes used − free minutes$400 - 200 = 200 \text{ min}$
   2. Step 2: Charge for the extra minutes, in dollars (cents ÷ 100)$\dfrac{200 \times 8}{100} = 16$
   3. Step 3: Add the monthly fee$18 + 16 = 34$The bill for March is $34.
4. Question 4Which phone plan is cheaper?

   The table shows two mobile phone plans. Chen Wei makes about 600 minutes of calls a month. Which plan is cheaper for Chen Wei?

   Plan	Monthly fee	Free talk time	Extra calls
   A	$20	300 min	15 cents per min
   B	$38	1000 min	8 cents per min

   Show the worked solution

   1. Step 1: Plan A: monthly fee + extra minutes × rate (in dollars)$\text{Plan A: } 20 + \dfrac{(600 - 300) \times 15}{100} = 65$
   2. Step 2: Plan B: monthly fee + extra minutes × rate (in dollars)$\text{Plan B: no extra minutes, so } 38$
   3. Step 3: Compare the two costsPlan B is cheaper for Chen Wei.
5. Question 5A utilities bill with GST

   The table shows a household's usage of utilities in a month. 9% GST is added to the total charges. Find the total amount payable, correct to the nearest cent.

   Service	Usage	Rate
   Electricity	380 kWh	$0.30 per kWh
   Water	14 m³	$1.50 per m³
   Gas	40 kWh	$0.22 per kWh

   Show the worked solution

   1. Step 1: Each charge = usage × rate (in dollars)$\text{Electricity: } 380 \times 0.30 = 114$$\text{Water: } 14 \times 1.50 = 21$$\text{Gas: } 40 \times 0.22 = 8.80$
   2. Step 2: Add the charges$114 + 21 + 8.80 = 143.80$
   3. Step 3: Add 9% GST$143.80 \times \dfrac{109}{100} = 156.742$$\approx 156.74$ (to the nearest cent)The total amount payable is $156.74.