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John compiled a table showing the amount of water used in his own household over the course of a week - Leaving Cert Mathematics - Question c - 2016

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John compiled a table showing the amount of water used in his own household over the course of a week. He recorded the number of litres required for each activity an... show full transcript

Worked Solution & Example Answer:John compiled a table showing the amount of water used in his own household over the course of a week - Leaving Cert Mathematics - Question c - 2016

Step 1

Complete the table to show the number of litres used for the various activities and the total number of litres used in the week.

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Answer

To find the number of litres used for each activity, multiply the water required per activity by the frequency.

  • One Bath: 80 litres × 3 = 240 litres
  • One Shower: 125 litres × 20 = 2500 litres
  • Brushing Teeth with Tap Running: 6 litres × 32 = 192 litres
  • One WC Flush: 6 litres × 60 = 360 litres
  • One Use of Washing Machine: 45 litres × 8 = 360 litres
  • One Use of Dishwasher: 20 litres × 7 = 140 litres
  • Washing One Car with a Bucket: 10 litres × 1 = 10 litres
  • Hosepipe: 9 litres × 15 = 135 litres

Now, sum all these values to get the total:

Total = 240 + 2500 + 192 + 360 + 360 + 140 + 10 + 135 = 3937 litres.

Step 2

If water were charged at £1.85 per 1000 litres, find what John’s household would pay for the water used in one year if the household uses the same amount of water each week.

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Answer

To calculate the annual cost of water, first find the weekly cost:

  • Total water usage per week = 3937 litres
  • Cost per litre = £1.85 / 1000 = £0.00185
  • Weekly cost = 3937 × £0.00185 = £7.27145

Now, multiply by the number of weeks in a year:

Annual cost = £7.27145 × 52 = £378.74.

Step 3

Find John’s total bill for this water if VAT were to be included at a rate of 13.5%.

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Answer

First, calculate the total cost before VAT:

  • Total cost = £378.74

Now, calculate VAT:

  • VAT = 13.5% of £378.74 = £378.74 × 0.135 = £51.2024

Total bill including VAT = £378.74 + £51.2024 = £429.94.

Step 4

If water were charged at £1.85 plus VAT at 13.5% per 1000 litres, find the number of litres of water he could purchase for £260.

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Answer

To determine how many litres John could purchase for £260, first find the cost per litre including VAT:

  • Cost per litre excluding VAT = £1.85 / 1000 = £0.00185
  • VAT per litre = 0.135 × £1.85 / 1000 = £0.00024975
  • Total cost per litre = £0.00185 + £0.00024975 = £0.00209975

Next, calculate the number of litres John could buy for £260:

Number of litres = £260 / £0.00209975 ≈ 123,825 litres.

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