A group of people went to a restaurant - Edexcel - GCSE Maths - Question 15 - 2019 - Paper 3

From those who chose soup, we can designate that if $y$ is the number of people who chose soup, we can express it as:

• The number of people who chose lasagne as $\frac{5}{8}y$
• The number of people who chose curry as $\frac{3}{8}y$
• Since $y = 2x$, the number who chose lasagne is:

$\frac{5}{8} (2x) = \frac{10}{8}x = \frac{5}{4}x$

• And for curry:

$\frac{3}{8} (2x) = \frac{6}{8}x = \frac{3}{4}x$

For the prawns, we denote the number of people who chose prawns as $3x$. Therefore, we can express:

• The number of people who chose lasagne as $\frac{1}{6} (3x) = \frac{1}{2}x$
• The number of people who chose curry as $\frac{5}{6} (3x) = \frac{5}{2}x$

Now we can combine the total number of people who chose curry from both starters:

• From soup: $\frac{3}{4}x$
• From prawns: $\frac{5}{2}x$

The total number who chose curry is:

$\frac{3}{4}x + \frac{5}{2}x = \frac{3}{4}x + \frac{10}{4}x = \frac{13}{4}x$

To find the fraction of people who chose curry, we take this total and divide it by the total number of people ($5x$):

$\frac{\frac{13}{4}x}{5x} = \frac{13}{20}$ Thus, the fraction of people who chose curry is rac{13}{20}.