Discussion » My Maths Is Rusty

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Posted by cal, 17:43, 4th November 2002:
 
I was given a mathematical problem which seems really simple, but took me AGES. Can anyone do better:

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Apples are worth £1 and bananas are worth £2. They can be freely exchanged.

After doing some exchanging, I now have 4 apples and 5 bananas.

I originally had 60% apples - how many apples and bananas did i start with?


The generalisation is what we're after:

Assuming apples are worth 'a' and bananas are worth 'b', and i originally had 'k' percent apples, find an equation for the original number of apples (x1) and bananas (y1) in terms of the current number of apples (x2) and bananas (y2).

Given this equation, you should be able to find x1 (and then y1), given that a=1, b=2, k=60, x2=4 and y2=5.

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Posted by Sul, 20:21, 4th November 2002:
 
I know, I know :D

Mail on its way to cal so I dont ruin it for everyone else
Posted by cal, 20:34, 4th November 2002:
 
no worries - sul has missed the point.

the example numbers are very very easy to solve in your head.

it's the formula that's needed
Posted by Victor Menendez, 20:36, 4th November 2002:
 
Pah, sul did it in 5 mins, shame on you cal ;)
Posted by reitsma, 21:54, 4th November 2002:
 
total cash = 4a + 5b
= 4 + 10

3na 2nb = 14
where a = apples (1)
b = banananananas (2)
n = a number.

3n + 2n2 = 14

7n = 14

n = 2

therefore

6a + 4b = 14

which is correct, yes?
Posted by cal, 23:24, 4th November 2002:
 
nope, still just solving it for the case i gave. i recieved the correct solution via email from David Wasserman. Slightly different to my own solution, but still correct. i'll post in in a few days time to give others a chance
Posted by Sul, 00:34, 5th November 2002:
 
"...find an equation for the original number of apples (x1) and bananas (y1) in terms of the current number of apples (x2) and bananas (y2)."

Well I did think of this originally but I think it's waaaay too general:

(x1*a)+(y1*b)=(x2*a)+(y2*b)

lol :D
Posted by cal, 08:24, 5th November 2002:
 
well, it's a starting point

since we know the values of a,b,x2 and y2, we need an equation for x1 in terms of the variables we know (you'll need k in there too)
Posted by sanchez, 12:32, 15th November 2002:
 
easy.... 6 apples, 4 bananas.
Posted by erasmus, 10:39, 20th November 2002:
 
1. You currently have 4 apples and 5 bananas
2. You had 60% apples
3. apples are worth 1 and bananas are worth 2
4. you can't have fractions of an apple/banana.

so you have less apples than you did before.
sell a banana for 2 and get 2 apples.
and you have 6 apples, 4 bananas
which makes 60%
Equations just make thinks too complicated.

tho you could have 3 apples and 2 bananas and
7 pounds.
Posted by cal, 11:25, 20th November 2002:
 
ooh, i'd forgotten about this thread.

My solution is here: www.iamcal.com/files/fruit.txt

The script I ended up using is here: www.iamcal.com/files/fruit_pl.txt

I also made a spreadsheet to do it automagically: www.iamcal.com/files/fruit.xls

David Wasserman offered another solution which can be found here: www.iamcal.com/files/fruit2.txt
Posted by Grim..., 12:40, 20th November 2002:
 
I fear David's answer...
Posted by cal, 13:05, 20th November 2002:
 
it's very similar to mine, but without all the intermediate steps shown
Posted by detergent_drinker, 18:20, 2nd December 2002:
 
aargh! i do enough maths at college
Posted by chandler, 21:13, 2nd December 2002:
 
I did Maths and Further Maths at A-level. Further Maths is pointless in the real world btw. Its all nonsense, made up by sick sick people, who don't think that the numbers -1000000 to 1000001 are enough and have to invent new crappy square root of minus 1 numbers and rubbish like that.

Anyway. There you go.
Posted by Gary, 21:29, 2nd December 2002:
 
Me and Maths do not get on very well. It took me three or four attempts to pass the first year Maths module at Uni. I finally passed the bloody thing - in my final year!
Posted by cal, 21:46, 2nd December 2002:
 
chay: i did a level maths and further maths too. i have a few friends doing maths degrees - utter madness
Posted by chandler, 08:16, 3rd December 2002:
 
i never could get my tutor to explain the point of futher maths. he would always say "oh well this bit isnt very useful at the moment, but one day it might be." in which case why not wait till then to actually learn the stuff :)
Posted by cal, 09:46, 3rd December 2002:
 
i've used certain things from further maths in my work. mainly it's useful if you want to teach further maths.
Posted by chandler, 09:47, 3rd December 2002:
 
:) but to do that you have to grow a big beard
Posted by cal, 09:51, 3rd December 2002:
 
most of my further maths teachers were women :/
Posted by chandler, 09:53, 3rd December 2002:
 
and your point is?

Actually I was the only one doing further maths so I had 1 to 1 tuition. Didnt help though :)
Posted by cal, 09:56, 3rd December 2002:
 
didya pass?
Posted by chandler, 09:57, 3rd December 2002:
 
I got an A in Maths. but a D in further, sniffle. My brain just couldn't accept that I wanted to learn something that I would never use. I think I need to know that something is going to be useful before I can dedicate time and brain power to it. as I said, I was never convinced that Further Maths was actually useful! :)
Posted by detergent_drinker, 10:14, 3rd December 2002:
 
god damn u guys are genius! i have enough trouble with getting a D in A-level maths.
Posted by Grim..., 12:20, 3rd December 2002:
 
Does that mean you got a D, or you think your going to get one?
Posted by Grim..., 12:21, 3rd December 2002:
 
Cal - who was your further Maths teacher? I had Mr Carradice, Mr Sommerfield and that woman who was head of maths whose name I forget - Procter?
Posted by cal, 12:43, 3rd December 2002:
 
i had:
proctor, dobson, gardner (ladies)
carradice, somerfield, major (men)