Higher June 2022 Paper 2 Q8
8 Behnaz makes 300 celebration cards so that
\[\begin{array}{c}\text{number of}\\ \text{birthday cards}\end{array} : \begin{array}{c}\text{number of}\\ \text{anniversary cards}\end{array} : \begin{array}{c}\text{number of}\\ \text{congratulations cards}\end{array} = 7:5:3\]\(\dfrac{2}{5}\) of the birthday cards have numbers on them.
36% of the anniversary cards have numbers on them.
None of the congratulations cards have numbers on them.
Work out what fraction of the 300 cards have numbers on them.
Give your answer in its simplest form.
(5)
| Scheme | Marks |
|---|---|
300 ÷ (7 + 5 + 3) (= 20) clear correct use of 7 + 5 + 3 ( = 15) eg division at the end by 15 \(\left(\dfrac{\text{``}{2.8}\text{''} + \text{``}{1.8}\text{''}}{15}\right)\) or correct use of 15 in a fraction eg \(\dfrac{2}{5} \times \dfrac{7}{15}\) | M1 |
\(\dfrac{2}{5} \times (7 \times \text{``}{20}\text{''})\;(= 56)\) oe eg \(0.4 \times \text{``}{140}\text{''}\;(= 56)\) or \(\dfrac{2}{5} \times 7\left(= \dfrac{14}{5} = 2.8\right)\) eg \(\dfrac{2}{5} \times \dfrac{7}{15}\left(= \dfrac{14}{75} = 0.186\ldots\right)\) | M1 |
0.36 × (5 × “20”)(=36)[from working] or 0.36 × 5 (= 1.8) eg \(\dfrac{36}{100} \times \dfrac{5}{15}\left(= \dfrac{180}{1500} = 0.12\right)\) oe | M1 |
\(\dfrac{\text{``}{56}\text{''} + \text{``}{36}\text{''}}{300}\left(= \dfrac{92}{300}\right)\) or eg \(\left(\dfrac{\text{``}{2.8}\text{''} + \text{``}{1.8}\text{''}}{15}\right)\) or \(\dfrac{\dfrac{14}{5} + \dfrac{9}{5}}{15}\) \(\text{``}{\dfrac{14}{75}}\text{''} + \text{``}{\dfrac{180}{1500}}\text{''}\) | M1 |
| \(\dfrac{23}{75}\) | A1 |
| (5) | |
| (5 marks) |
Notes
M1: (no mark for “15” unless it is used correctly)
use of 7 × 20 or 140 or 5 × 20 or 100 in further work assumes this mark
M1: finding \(\dfrac{2}{5}\) of the number of birthday cards
or
\(\dfrac{2}{5}\) of the share of 7 or \(\dfrac{2}{5}\) of fraction of amount
M1: finding 36% of anniversary cards
Or
36% of the share of 5 or 36% of fraction of amount
M1: for any fraction from correct working that isn’t simplified
or
30.66..% or 0.3066...