4 ms·
Without the trick you get: Coffee concentration before first,second,third,fourth drinking = 1,x,y,z x = 1/2 y = x*2/3 + 0*1/3 = 1/3 z = y*5/6 + 0*1/6 =
by dan-robertson 5y ago
Without the trick you get:
Coffee concentration before first,second,third,fourth drinking = 1,x,y,z
x = 1/2
y = x*2/3 + 0*1/3 = 1/3
z = y*5/6 + 0*1/6 = 5/18
Coffee drunk = 1/2 + 1/3 x + 1/6 y + z
= 1/2 + 1/6 + 1/18 + 5/18
= 3/6 + 1/6 + 2/6
= 1
Milk drunk = 0 + 1/3(1-x) + 1/6(1-y) + (1-z)
= 1/6 + 2/18 + 13/18
= 1/6 + 5/6
= 1
Which is a bit fiddly but hardly impossible. I think there is pedagogical value in doing the algebra accurately and I think it is annoying enough that the trick seems useful and memorable when it is pointed out. The trick is also quite broadly applicable to physics problems where there is conservation of some quantity.
- andi999 5y agoIt is not impossible but I dont think generally grade 5-6 students have a chance to solve this (of course it depends how much training they received)
- dan-robertson 5y agoYeah I think the examples given are probably examples of hard exercises or the grades are a poor translation (maybe grade 1 has 6 year olds, for example.) Another solution is with geometry: Start with a 1x1x1 cube of coffee. Remove top half and replace with milk. Now remove left third of resulting combined shape (leaving a 2/3 x 1/2 x 1 cuboid of coffee). Now remove front sixth (leaving a 2/3 x 1/2 x 5/6 cuboid). Now drink it all. Now add up the volumes of the shape and write down the answer.