1MA0 Foundation June 2012 Paper 2 Q28
*28 Henry is thinking about having a water meter.
These are the two ways he can pay for the water he uses.
| Water Meter | No Water Meter |
|---|---|
| A charge of £28.20 per year plus 91.22p for every cubic metre of water used 1 cubic metre = 1000 litres | A charge of £107 per year |
Henry uses an average of 180 litres of water each day.
Henry wants to pay as little as possible for the water he uses.
Should Henry have a water meter? (5)
| Working | Answer | Mark | Notes | ||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(180 \times 365 = 65700\) \(65700 \div 1000 = 65.7\) \(65.7 \times 91.22 = 5993.154\) \(5993.154 \div 100 + 28.20 = 88.13..\)
| Decision ( Should have a water meter installed) | 5 | Per year M1 for \(180 \times\) ‘365’ (=65700) M1 for “65700” \(\div 1000\) (=65.7 or 65 or 66) M1 for “65.7” \(\times 91.22\) (=5993.....) A1 for answer in range (£)87 – (£)89 C1(dep on at least M1) for conclusion following from working seen OR (per day) M1 for \(107 \div\) ‘365’ (=0.293…) M1 for \(180 \div 1000 \times 91.22\) (=16.4196) M1 for \(28.2 \div\) ‘365’ + ‘0.164196’ (units must be consistent) A1 for 29 – 30(p) and 24– 24.3(p) oe C1(dep on at least M1) for conclusion following from working seen OR M1 for \((107 - 28.20) \div 0.9122\) (=86.384..) M1 for ’86.384..’ \(\times 1000\) (=86384.5…) M1 for ‘365’ \(\times 180\) (=65700) A1 for 65700 and 86384.5.. C1(dep on at least M1) for conclusion following from working seen NB : Allow 365 or 366 or \(52 \times 7\) (=364) or \(12 \times 30\) (=360) or \(365\frac{1}{4}\) for number of days |