Numeracy Higher June 2019 Unit 2 Q10
10. Holly wants to buy a new house in Cardiff.
She knows that Land Transaction Tax will be added to the price of the house.
Land Transaction Tax rates are shown below:
- pay nothing on the first £180 000 of the price of the house,
- pay 3·5% on the part of the price of the house that is above £180 000 and up to and including £250 000,
- pay 5% on the part of the price of the house that is above £250 000 and up to and including £400 000.
(a) Show that the Land Transaction Tax payable on a house costing £255 000 is £2700. [2]
(b) The most Holly can afford to spend, including Land Transaction Tax, is £327 000.
Let \(x\) be the highest price of house that Holly can afford.
Write an equation in \(x\) and solve it to calculate the highest price of house that Holly can afford. [5]
| Scheme | Marks | Comments |
|---|---|---|
| 0.035 × (250 000 – 180 000) + 0.05 × (255 000 – 250 000) (= 2450 + 250 = 2700) | B2 | B1 for 0.035 × (250 000 – 180 000) (= 2450) OR B1 for 0.05 × (255 000 – 250 000) (= 250) |
| Scheme | Marks | Comments |
|---|---|---|
| Sight of 0.05 × (x – 250 000) = 0.05x – 12 500 | B1 B1 | May be embedded in their equation May be embedded in their equation |
| x + 2450 + 0.05x – 12 500 = 327 000 or equivalent | M1 | No further marks unless an appropriate equation seen FT ‘their 0.035(250 000 – 180 000)' AND ‘their 0.05 × 250 000’ |
| 1.05x – 10 050 = 327 000 OR 1.05x = 337 050 | m1 | |
| x = (£)321 000 | A1 | CAO If no marks awarded, award SC2 for x = (£)321 000 If B1 only previously awarded, replace with SC2 for x = (£)321 000 Note: If a candidate uses x as being the amount over £250 000, then award B0B0 followed by M1 for 1.05x + 180 000 + (1.035 x 70 000) = 327 000 or equivalent A1 for x = (£) 71 000 A1 for (£) 321 000 |
Alternative
Alternative method:
| Scheme | Marks | Comments |
|---|---|---|
| Sight of 0.05 × (x – 255 000) = 0.05x – 12 750 | B1 B1 | May be embedded in their equation May be embedded in their equation |
| x + 2700 + 0.05x – 12 750 = 327 000 | M1 | No further marks unless an appropriate equation seen FT ‘their 2700' AND ‘their 0.05 × 255 000’ |
| 1.05x – 10 050 = 327 000 OR 1.05x = 337 050 | m1 | |
| x = (£)321 000 | A1 | CAO If no marks awarded, award SC2 for x = (£)321 000 If B1 only previously awarded, replace with SC2 for x = (£)321 000 Note: If a candidate uses x as being the amount over £255 000, then award B0B0 followed by M1 for 1.05x + 180 000 + 75 000 + 2700 = 327 000 A1 for x = (£) 66 000 A1 for (£) 321 000 |