Higher June 2017 Paper 2 Q13
13.
(a) Roberto buys 3 kg of carrots and 8 kg of turnips.
He plans to make soup.
The recipe he plans to use says,
He plans to make soup.
The recipe he plans to use says,
‘The ratio of carrots : turnips : onions is 5 : 3 : 2.’
Roberto plans to use all of the carrots.- How many kilograms of turnips will he have left?
- How many kilograms of onions will he need? [5]
(b) A farm shop sells carrots and turnips.
Hadley buys 4 kg of carrots and 5 kg of turnips.
Daisy buys 3 kg of carrots and 8 kg of turnips.
Hadley spends £4.25 and Daisy spends £5.61.
Use an algebraic method to calculate the total cost of 1 kg of carrots and 10 kg of turnips.
You must show your working. [5]
Hadley buys 4 kg of carrots and 5 kg of turnips.
Daisy buys 3 kg of carrots and 8 kg of turnips.
Hadley spends £4.25 and Daisy spends £5.61.
Use an algebraic method to calculate the total cost of 1 kg of carrots and 10 kg of turnips.
You must show your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| (Turnips used) 3 × 3 ÷ 5 or 6 × 3 ÷ 10 or (Turnips left over) 8 – 3 × 3 ÷ 5 or 8 – 6 × 3 ÷ 10 | M1 | Allow equivalent in g for possible M1, A1, A0 only |
| 1.8 (kg) turnips needed 6.2 (kg) turnips left over | A1 A1 | CAO CAO |
| (Onions needed) 3 × 2 ÷ 5 or 6 × 2 ÷ 10 or 1.8 × 2 ÷ 3 | M1 | FT ‘their 1.8’ Allow equivalent in g for possible M1, A0 only |
| 1.2 (kg) | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| \(4c + 5t = 4(.)25\) and \(3c + 8t = 5(.)61\) | B1 | Both equations given, \(c\) & \(t\) may be other letters, words are accepted FT provided at least one equation is correct and the other in an equivalent format, provided equivalent level of difficulty. |
| Method to eliminate variable, e.g. equal coefficients and shows intention to subtract | M1 | Allow 1 error in one term, not one with equal coefficients \(c = (0.)35\) or \(t = (0.)57\) |
| First variable | A1 | |
| Second variable | A1 | FT their first variable provided M1 previously awarded |
| (£)6.05 | B1 | If units are given they must be correct, allow £6.05p FT ‘their (0.)35’ + 10× ‘their (0.)57’ provided M1 awarded Unsupported answers, no marks |
| (10) |