Clearly, readers got weary of the TNDOT exams (and I still have some tidying up to do). There is also still a bit to say about the Two Ladies Problem. So, I’m reluctant to keep going. But, Red Five has thrown the problem below at me.
The problem comes from an 1858 Cambridge exam, for “students who are not more than 18 years of age” and “who are not members of the university”, which presumably amounted to an entrance exam for senior school students. This particular exam was on “Arithmetic, Algebra, Trigonometry and Land-surveying”. Go figure.
Here is the problem.
A, B and C rent a field for £180. A puts in 12 horses for 5 months, and 45 sheep for 3 months. B puts in 15 oxen for 6 months, and 54 sheep for 2 months. C puts in 6 horses and 47 oxen for 3 months. Now 4 horses and 3 sheep together eat as much as 5 oxen and 1 horse; also two oxen eat as much as 7 sheep; how much of the rent should A, B and C pay respectively?
Not that hard?
Not showing working, but A and B about 53 pounds each, and C 73 pounds.
For some reason I was reminded of the (silly?) old problem:
“A mum is 21 years older than her kid. In 6 years, she’ll be 5 times older than her kid. Where is the mother?”
Or the science joke:
Why did the ox hide?
Because the ass hid.
Thanks, LD. I didn’t look but, yes, I assumed the problem was pretty easy. But I also thought it was interesting for that reason. My guess is that a Y7 or Y8 student has the skills for solving this problem but also most of them have a snowflake’s chance of doing so, or would even attempt to do so.
When you say “about 53 pounds each” – can you be more specific?
I’m not convinced it is easy enough for a Year 7/8 student unless they are given some guidance. By Year 9 maybe when most will have seen simultaneous equations.
53,60;53,30 and 73,10.
I think they will have the skills to do the calculations but most of them lack the strategic competence how to approach the problem and the perseverance to keep working towards the solution.
I think it is quite time consuming to teach this level of problem solving skill at that age.
I agree students won’t have the perseverance in general, but I think the results are 54.43 pounds, 52.93 pounds and 72.64 pounds, are they not? (In 1858 they would have had to convert to pounds/shillings/pence. Can’t see students trying that now.)
Thanks, Peter. One would naturally keep the answer as fractions of a pound. That may be nicer to then express in shillings and pence?
You’re right Marty. I was rushing. Fractions would be more useful. Thanks
LSD would be the most appropriate units for the answer.
One could develop simpler problems about ratios that are suitable for Year 7 students. I might try this on the weekend because we have just finished ratios with my Year 7 class.
My answer is that A should pay £ 53/10/10, B should pay £ 53/6/-, and C should pay £ 73/3/2. I did not go below pence – although in 1858 one might be expected to.
The key for me was to find an appropriate base unit; assuming that rent is proportional to the amount of feed consumed, I decided on sheep-months.
“Sheep-months”. That might well be the best phrase I have heard in a week!
I would assume that an approximate solution (to the nearest coin available) would suffice.
I still think it is a nice problem, despite comments suggesting it is “easy”
I have developed a set of simpler, similar problems for my Year 7 class tomorrow; naturally I changed the currency and I used “paddock” instead of “field”. Thanks for the inspiration.