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.

Question

Mathematics

Moises Christian

10 February, 11:59

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.

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Answers (1)

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Giggles · 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