Higher November 2019 Paper 3 Q14
14 A group of people went to a restaurant.
Each person chose one starter and one main course.
| starter | main course |
|---|---|
| soup | lasagne |
| prawns | curry |
the number of people who chose soup : the number of people who chose prawns = 2 : 3
Of those who chose soup,
the number of people who chose lasagne : the number of people who chose curry = 5 : 3
Of those who chose prawns,
the number of people who chose lasagne : the number of people who chose curry = 1 : 5
What fraction of the people chose curry?
You must show how you get your answer. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(\dfrac{13}{20}\) | P1 | for finding the fraction who chose either soup \(\left(\dfrac{2}{5}\text{ oe}\right)\) or chose prawns \(\left(\dfrac{3}{5}\text{ oe}\right)\) or for process to share any number in the ratio 2 : 3 eg \(100 \div (2 + 3) \times 2\ (= 40)\) |
| P1 | for a process that could lead to the proportion who chose lasagne or curry for either starter, eg sharing 40% (soup) in the ratio 5 : 3 or sharing 60% (prawns) in the ratio 1 : 5 or \(\dfrac{2}{5} \times \dfrac{5}{8}\) or \(\dfrac{2}{5} \times \dfrac{3}{8}\) or \(\dfrac{3}{5} \times \dfrac{1}{6}\) or \(\dfrac{3}{5} \times \dfrac{5}{6}\) or for continuing the process with their starting number to find the number who chose lasagne or curry for either starter | |
| P1 | for a complete process to find the proportion who chose curry for both starters, eg \(\left(\dfrac{2}{5} \times \dfrac{3}{8}\right) + \left(\dfrac{3}{5} \times \dfrac{5}{6}\right)\) or to find the number who chose curry for both starters for their starting number | |
| A1 | \(\dfrac{13}{20}\) or equivalent fraction |
Additional guidance
Starting number 100
Soup : Prawn 40 : 60
L : C 25 : 15 L : C 10 : 50
15 + 50 = 65 and \(\dfrac{15 + 50}{100}\)