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A group of people went to a restaurant - Edexcel - GCSE Maths - Question 16 - 2019 - Paper 3
Question 16
A group of people went to a restaurant. Each person chose one starter and one main course. | starter | main course | |----------|-------------| | soup | lasagn... show full transcript
Worked Solution & Example Answer:A group of people went to a restaurant - Edexcel - GCSE Maths - Question 16 - 2019 - Paper 3
Step 1
the number of people who chose soup : the number of people who chose prawns = 2 : 3
Answer
Let the total number of people be represented as ( x ). According to the information given, the number of people who chose soup is ( \frac{2}{5}x ) and the number who chose prawns is ( \frac{3}{5}x ).
Step 2
the number of people who chose soup, the number of people who chose lasagne : the number of people who chose curry = 5 : 3
Answer
Among the ( \frac{2}{5}x ) who chose soup, if we denote the number of people who chose lasagne as ( 5y ) and those who chose curry as ( 3y ), we have: [ 5y + 3y = \frac{2}{5}x \implies 8y = \frac{2}{5}x \implies y = \frac{2}{40}x = \frac{1}{20}x.] Thus, the number who chose lasagne is ( 5y = \frac{5}{20}x = \frac{1}{4}x ) and curry is ( 3y = \frac{3}{20}x).
Step 3
Of those who chose prawns, the number of people who chose lasagne : the number of people who chose curry = 1 : 5
Answer
For those who chose prawns, the number who chose lasagne is ( z ) and those who chose curry is ( 5z ). Therefore, we have: [ z + 5z = \frac{3}{5}x \implies 6z = \frac{3}{5}x \implies z = \frac{3}{30}x = \frac{1}{10}x.] This means ( 1z = \frac{1}{10}x ) for lasagne, and ( 5z = \frac{5}{10}x = \frac{1}{2}x ) for curry.
Step 4
What fraction of the people chose curry?
Answer
To find the total number of people who chose curry, add those who chose curry from both groups: [ \frac{3}{20}x + \frac{1}{2}x = \frac{3}{20}x + \frac{10}{20}x = \frac{13}{20}x. ] Now, the fraction of total people who chose curry is: [ \frac{\frac{13}{20}x}{x} = \frac{13}{20}. ] Thus, the final answer is ( \frac{13}{20} ) or equivalent fraction.