Saturday, October 22, 2011

math problem the price of milk

This is something that came up with me. I often buy a 4L jug of milk. I noticed that sometimes the milk goes bad before I finish it and I end up pouring some of it out.

So I thought I might buy 2L milk instead. Then I saw the prices:

4L milk: $5.69
2L milk: $3.99

which leads to the practical math problems.

1) how much (in litres) of a 4L jug can you pour out and still be better off than buying 2L

2) the main body of a 4L jug is around 8 inches high. assuming the entire 4L content fits in that 8 inches, how many inches can you pour out off the bottom of a 4L and still be ahead

we can assume that the buyer will always be able to finish a 2L milk. so as a baseline the 2L is always fully consumed with no losses

these should be solvable by a high school student or a better junior high. I'll let it sit for a couple of days then post the answer in the comments.

1 comment:

Rob said...

first work out the per litre price. this will also check that it's not some trick question where the 2L price is lower

the unit price of the 4L jug is $1.4225 / L

the unit price of the 2L jug is $1.995 / L

now to determine the break even point we determine how much milk we can drink for $5.69 such that it costs $1.995 / L.

The answer is 5.69 / 1.995 = 2.85 L.

The answer to question 1) is then 4 - 2.85 = 1.15 L. We can toss over a litre of a 4L jug and still be better off than buying a 2L jug. That suggests that in general people are buying way too many 2L milks when they would be better off buying the 4L size.

To answer question 2) we convert it to a percentage and project it over 8 inches. 1.15 / 4 = 28.7 percent

28.7 percent of 8 inches is 2.3. So you can toss over 2 inches and still be better off buying the 4L size.

So I've been right buying the 4L size even though I sometimes don't finish it all.