Question

At Mary's Café, cakes

cost four euros and
sandwiches are two
euros. Eight people
go to Mary's Café
and they all have
either a cake or a
sandwich. At the end of the day, Mary has
made twenty-two euros.
Let the number of cakes sold equal x and the
number of sandwiches equal y.
(i) Write two equations in terms of x and y.
(ii) Solve these equations simultaneously
to find how many cakes and how many
sandwiches Mary sold that day.

Answer 1

Great problem! Here's how we can solve it:

(i) We can write two equations based on the information provided:

x + y = 8 (total number of people)
4x + 2y = 22 (total amount of money made)

(ii) We can solve these equations simultaneously by using substitution or elimination. I'll use substitution:

x + y = 8
x = 8 - y (solve for x)

4x + 2y = 22
4(8 - y) + 2y = 22 (substitute x with 8 - y)
32 - 4y + 2y = 22 (simplify)
32 - 2y = 22
-2y = -10
y = 5 (solve for y)

x = 8 - y
x = 8 - 5
x = 3 (solve for x)

So Mary sold 3 cakes and 5 sandwiches that day.