Marianne has been collecting donations for her biscuit stall at the school summer fayre. There are some luxury gift tins of bisc
uits 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 recieved exactly 100 donations in total, with a collective value of £100, amd 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.
The problem conditions give rise to 2 equations in 3 unknowns. Let L, M, N represent the number of Luxury, Mini, and Normal packets sold. .. L +M +N = 100 . . . . . . the number of packets sold .. 5L +0.1M +N = 100 . . the value of donations These result in the relationships .. L = (9/40)M .. N = 100 -(49/40)M
There are three integer solutions in which the numbers are non-negative. .. (L, M, N) = (0, 0, 100) or (9, 40, 51) or (18, 80, 2)
If Marianne sold 100 normal packets, her stock would be "very low" compared to the others.
If Marianne sold 51 normal packets, her stock may be "very low" with respect to the others, depending on how many of each she started with. This might be the solution if we require non-zero numbers of all packets were sold.
