Foundation November 2019 Paper 1 Q18
18 Bob makes dry concrete by mixing cement, sand and stone in the ratio 1 : 2 : 3 by weight.
He buys the cement, sand and stone in bags as shown in this table.
| Weight of bag (kg) | Cost per bag (£) | |
|---|---|---|
| Cement | 25 | 5.50 |
| Sand | 20 | 2.00 |
| Stone | 15 | 3.90 |
He packs the dry concrete into 30 kg bags.
Bob buys just enough cement, sand and stone to make 50 bags of dry concrete.
(a) Show that Bob buys 500 kg of sand. [3]
(b) Bob sells the 50 bags of dry concrete for a total of £396.
Calculate Bob’s percentage profit. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 50 × 30 | 1 | Accept any correct method e.g. M1 for \(\dfrac{2}{1 + 2 + 3} = \dfrac{2}{6}\) | |
| \(\dfrac{50 \times 30}{1 + 2 + 3}\) [×1, 2 or 3] | 1 | M1 for \(\dfrac{2}{6} \times 50\) or 50/3 | watch for wrong method 50 x 20 = 1000. 1000÷2 = 500 |
| 2 × 250 = 500 | 1 | M1 for \(\dfrac{50}{3} \times 30 = 500\) Alternative method M1 for 30 ÷ 6 = 5 M1 for their (30 ÷ 6 ) × 2 M1 for 50 × 10 = 500 | Mark to candidates advantage |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 32 | 5 | M1 for \(\dfrac{250}{25}\) or \(\dfrac{500}{20}\) or \(\dfrac{750}{15}\) M1 for their 10 × 5.5[0] or their 25 × 2[.00] or their 50 × 3.9[0] M1 for their 10 × 5.5[0] + their 25 × 2[.00] + their 50 × 3.9[0] M1 for \(\dfrac{396}{\textit{their } 300}\) or \(\dfrac{396 - \textit{their } 300}{\textit{their } 300}\) Alternative method M1 for \(\dfrac{\frac{30}{6} \times 1}{25}\) or \(\dfrac{\frac{30}{6} \times 2}{20}\) or \(\dfrac{\frac{30}{6} \times 3}{15}\) or \(\dfrac{396}{50}\) M1 for 5.5[0] × their [0].2 or 2[.00] × their [0].5 or 3.9[0] × their 1 M1 for their (5.5[0] × [0].2) + their (2[.00] ×.[0].5) + their (3.9[0] × 1) M1 for \(\dfrac{7.92}{\textit{their } 6}\) or \(\dfrac{7.92 - \textit{their } 6}{\textit{their } 6}\) | M1 may be implied by 10 or 25 (no. of bags/part bags of cement, sand, stone) M2 may be implied by 55 and 195 (cost of cement, sand, stone) M3 may be implied by 300 or 6 nfww (total production cost) M1 may be implied by 0.2, 0.5 or 1 or 7.92 (no. of bags/part bags of cement, sand, stone or price of 1 bag) M2 may be implied by 1.1[0], 1[.00] or 3.9[0] (cost of cement, sand, stone for 1 bag) M3 may be implied by 6 nfww (total production cost of 1 bag) |