Question

Marianne has been collecting donations for her biscuit stall at the school summer fayre. There are some luxury gift tins of biscuits to be sold at £5 each, normal packets at £1 each, and mini-packs of 2 biscuits at 10p each. She tells Amy that she has received exactly 100 donations in total, with a collective value of £100, and that her stock of £1 packets is very low compared with the other items. Amy wants to work out how many of each item Marianne has. Show how she can do it.

Answer 1

First, we define variables:
x = luxury gift tins of biscuits
y = normal packets
z = mini-packs of 2 biscuits
We have the following system of equations:
x + y + z = 100
5x + y + 10z = 100
"her stock of £ 1 packets is very low compared with the other items"
So,
y = 0 (approximately).
answer:
Amy must solve the system of equations:
x + y + z = 100
5x + y + 10z = 100
y = 0
to know how many of each item Marianne has