Higher November 2020 Paper 1R Q10
10 Alex makes 80 cakes to sell.
He makes chocolate cakes, lemon cakes and fruit cakes where
\(\begin{matrix}\text{number of}\\ \text{chocolate cakes}\end{matrix} \;:\; \begin{matrix}\text{number of}\\ \text{lemon cakes}\end{matrix} \;:\; \begin{matrix}\text{number of}\\ \text{fruit cakes}\end{matrix} \;=\; 3 : 2 : 5\)
Alex sells
- all of the chocolate cakes
- \(\dfrac{3}{4}\) of the lemon cakes
- \(\dfrac{7}{8}\) of the fruit cakes
The profit he makes on each cake he sells is shown in the table.
| Type of cake | Profit per cake he sells |
|---|---|
| chocolate | £2.00 |
| lemon | £1.70 |
| fruit | £2.40 |
Work out the total profit that Alex makes from the cakes he sells.
(5)
| Scheme | Marks |
|---|---|
| e.g. \(\dfrac{3}{\text{“}{10}\text{”}} \times 80 (= 24)\) or \(\dfrac{2}{\text{“}{10}\text{”}} \times 80 (= 16)\) or \(\dfrac{5}{\text{“}{10}\text{”}} \times 80 (= 40)\) | M2 |
| e.g. “16” × \(\dfrac{3}{4}\) × 1.7(0) (= 20.4(0)) or “40” × \(\dfrac{7}{8}\) × 2.4(0) (= 84) | M1 |
e.g. “24” × 2 (= 48) and “16” × \(\dfrac{3}{4}\) × 1.7(0) (= 20.4(0)) and “40” × \(\dfrac{7}{8}\) × 2.4(0) (= 84) | M1 |
| 152.4(0) | A1 |
| (5) | |
| (5 marks) |
Notes
M2: for a complete method to find the number of chocolate cakes or lemon cakes or fruit cakes
“10” comes from 3 + 2 + 5
(M1 for correct use of the ratio
e.g. 80 ÷ “10” (= 8))
M1: for a method to find the profit for lemon cakes or fruit cakes
M1: for a method to find the profit for all 3 cakes