4MA0 Foundation January 2018 Paper 1R Q23
23 There are 320 students at a school.
\(\dfrac{5}{8}\) of these students are girls.
\(\dfrac{3}{4}\) of the girls have blue eyes.
\(\dfrac{2}{3}\) of the boys have blue eyes.
What fraction of the students at the school have blue eyes?
(4)
| Scheme | Marks |
|---|---|
\(\dfrac{5}{8} \times \dfrac{3}{4}\left(= \dfrac{15}{32}\right)\) or \(\dfrac{5}{8} \times 320\) (= 200) or \(\left(1 - \dfrac{5}{8}\right) \times 320\) (= 120) | M1 |
\(\left(1 - \dfrac{5}{8}\right) \times \dfrac{2}{3}\left(= \dfrac{6}{24}\right)\) or \(\dfrac{3}{4} \times \text{'}200\text{'}\) (= 150) oe and \(\dfrac{2}{3} \times \text{‘}120\text{’}\) (= 80) oe | M1 |
\(\text{‘}\dfrac{15}{32}\text{’} + \text{‘}\dfrac{6}{24}\text{’}\) oe or \(\dfrac{\text{'}150\text{'} + \text{'}80\text{'}}{320}\) oe | M1 |
| \(\dfrac{23}{32}\) | A1 |
| (4) |
Notes
M1: for a complete method
A1: oe