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An ancient Celtic chicken farmer wished to produce a gift for his wife. The gift was worth 2 horses. At the local market, 3 horses were worth 5 cows, 1 cow was worth 5 hogs, 3 hogs were worth 4 goats, 1 goat cost 9

chickens. How much was the gift going to cost the farmer, who had to pay in chickens?

Cheesecat wrote:chicken framer

The man frames chickens?

He is clearly very sick, and math shouldn't be his first priority.

Medium of Death wrote:

Cheesecat wrote:chicken framer

The man frames chickens?

He is clearly very sick, and math shouldn't be his first priority.

I meant chicken farmer.

IGNORE THAT PREVIOUS NONSENSE: TIME FOR BED.

200 finely framed chickens is my guess.

Medium of Death wrote:horse = x
cow = y
hogs = z
goats = v
chickens = q

3x = 5y
y = 5z
3z = 4v
v = 9q

IGNORE THAT PREVIOUS NONSENSE: TIME FOR BED.

Thank you.

Chicken Frames?

Must be a KFC executive.

African or European Chickens?

Pretty sure it's 200 chickens. There's a much easier way than that posted by Medium of Death using fractions.

N chickens = 2 horses * 5 cows * 5 hogs * 4 goats * 9 chickens 3 horses 1 cow 3 hogs 1 goat
(Imagine those are fractions)

As you can see, each label (variable) cancels (horses, cows, hogs, goats) leaving 2 * 5/3 * 5/1 * 4/3 * 9/1 chickens

EDIT: Is that easier?

Cheesecat wrote:An ancient Celtic chicken farmer wished to produce a gift for his wife. The gift was worth 2 horses. At the local market, 3 horses were worth 5 cows, 1 cow was worth 5 hogs, 3 hogs were worth 4 goats, 1 goat cost 9

chickens. How much was the gift going to cost the farmer, who had to pay in chickens?

Well, I would reckon that people wouldn't want to trade partial chickens or partial cows for whole horses. He would get 3 horses for 5 cows, 3/5 gives us the idea that each cow is worth 0.6 of a horse. If we wanted two horses we would need 3.33 cows. 1 cow is 5 pigs so we need 3.33x5 to need 16.67 pigs. One goat is 0.75 of a pig and we need 16.67 pigs. We need 22.23 goats to make the trade. If 1 goat is worth 9 chickens we would need 200.04 chickens.

However, like I said people would probably not be willing to trade partial animals so its much easier. He needs 5 cows for 3 horses, he also needs 5 hogs for 1 cow. That means we need 25 hogs altogether, unfortunately 25 is not divisible by three and we would then need to get 27 hogs, which means we need to multiply the number of goats by 9 (27/9 is three). So we need 36 goats, each goat is worth 9 chickens so 36x9 makes 324 whole chickens total and he would have 3 whole horses.

Scientifically its written like this:

2horses x 5cows/3horses x 5hogs/1cow x 4goats/3hogs x 9chickens/1goat. The values(horses, cows, etc cancel out until we are left with only one value, that being 'chickens', thanks to division and multiplication rules).

Chibi Bodge-Battle wrote:African or European Chickens?

He's Celtic so probably European Chickens.

v=9
3z=4(9)
z=12
y=5(12)
y=60
3x=5(60)
x=100
100 per horse
x2
200 chickens for the gift

Am I right? I am mentaly fried, just studied for my physics exam.

if you say

q = 1

It pretty much solves itself, surely?

I didn't want to spoil all the 'fun' though

Trick question. The farmer kicks the gift seller in the crotch and nicks the gift whilst the vendor is occupied.

biccat wrote:Pretty sure it's 200 chickens. There's a much easier way than that posted by Medium of Death using fractions.

N chickens = 2 horses * 5 cows * 5 hogs * 4 goats * 9 chickens 3 horses 1 cow 3 hogs 1 goat
(Imagine those are fractions)

As you can see, each label (variable) cancels (horses, cows, hogs, goats) leaving 2 * 5/3 * 5/1 * 4/3 * 9/1 chickens

Medium of Death wrote:EDIT: Is that easier?

*Turns Brain On*

Yes, yes it is.

Cheesecat wrote:How much was the gift going to cost the farmer, who had to pay in chickens?

Also, you could be a jerk and say "two horses" because the question doesn't ask for units.

We had fun with this in undergrad. Units like "rods per fortnight" (instead of MPH or mps) made a regular appearance.

42, because it's the answer to everything.

halonachos wrote:Well, I would reckon that people wouldn't want to trade partial chickens or partial cows for whole horses.

But that only holds if you assume he needs to trade his chickens for goats, then take all those goats and trade them hogs, then take all those hogs and trade them for cows and so on, rather than just straight up paying in chickens and letting market determine equivalents set the trade off price for each product.

In fact, feth it, my answer is 1 chicken. Because this is the ancient world and assumptions of perfactly balanced trading markets are completely inappropriate. I mean, unless there are trading agents active in the market trying to make arbitrage profits we just can't make that assumption. Never mind assumptions of perfect information.


But yeah, the actual answer is 200 chickens.
Gift equals 2 horses.
3 horses equals 5 cows. Therefore the gift is worth 3.33 cows.
1 cow equals 5 hogs. Therefore the gift is worth 16.67 hogs.
3 hogs equals 4 goats. Therefore the gift is worth 22.22 goats.
1 goat equals 9 chickens. Therefore the gift is worth 200 chickens.


I also think you should follow up on answering this question with an essay on why the ancient Celts would have been much better off using teef as a currency.

sebster wrote:

halonachos wrote:Well, I would reckon that people wouldn't want to trade partial chickens or partial cows for whole horses.

But that only holds if you assume he needs to trade his chickens for goats, then take all those goats and trade them hogs, then take all those hogs and trade them for cows and so on, rather than just straight up paying in chickens and letting market determine equivalents set the trade off price for each product.

In fact, feth it, my answer is 1 chicken. Because this is the ancient world and assumptions of perfactly balanced trading markets are completely inappropriate. I mean, unless there are trading agents active in the market trying to make arbitrage profits we just can't make that assumption. Never mind assumptions of perfect information.


But yeah, the actual answer is 200 chickens.
Gift equals 2 horses.
3 horses equals 5 cows. Therefore the gift is worth 3.33 cows.
1 cow equals 5 hogs. Therefore the gift is worth 16.67 hogs.
3 hogs equals 4 goats. Therefore the gift is worth 22.22 goats.
1 goat equals 9 chickens. Therefore the gift is worth 200 chickens.


I also think you should follow up on answering this question with an essay on why the ancient Celts would have been much better off using teef as a currency.

Maybe we should make the assumption that the ancient Celt has a sword and the sword is equal to 2 horses and 200 chickens and whatever else the other guy has.

I guess I work this like a computer compiler would work it, backwards:

1 goat = 9 chickens -> 1 goat : 9 chickens
3 hogs = 4 goats -> 3 hogs : 4 goats : 36 chickens
1 cow = 5 hogs -> 1 cow : 5 hogs : 5/3 hogs : 60 chickens
3 horses = 5 cows -> 3 horses : 5 cows : 25 hogs : 300 chickens
2 horses is the gift and 3 horses = 300 chickens, therefore 2/3 of 300 chickens is 200.

And this is where an augmented matrix comes in real @%%#$@%$@# handy.

No manipulating and re-writing everything, and everything settles to a nice number of how much of everything you need. I will try and see if I can provide an explanation later on tonight or at the end of the week.

matrices are incredibly helpful tools. They take your linear systems, and make it much easier to manipulate them to find solutons. What matrices do, is take your equations and simplify them, so that when you finish working with them, you have A=1, b=2. c=4, d=8, etc, for each variable when you finish. Normal rules of math aply (when assigning variables, define what each variable represents.... dont divide by zero, etc.)

First, set up your equations vertically, so that each element has a unique variable, and a coeficient, as equivalent to something else.

Then, take the coeficients, and plug them into a square. For your interest, a solution is possible if you have as many equations as you have variables. You then line your equations up so that the same variables appear in the same column, adding coefficients of 0 for each variable that does not bear any relevanced for that equation. Then, draw a left square bracket. Punch in your coefficients, from left to right for each variable (dont bother with the variable), then draw a vertical line, and in your case, everything should equate to zero if you've done your equations right, so your vectors should all be zero except for your last one which is 1G=9 chickens. Chickens aren't a variable though, because the farmer has them... all you do now is manipulate your rows by dividing each row by a number, or adding/subrtracting rows from eachother, such that, from left to right, you end up with a diagonal of 1's and in the end, a zero occupies all other squares in the coefficient matrix (the vector matric, the colmn at the right end, will respond to the operations)

Now, imagine the top-most equation is (1 Gift = 2 horses) => ( -1 gift + 2 Horses = 0). The equation in the bottom right is (1 goat = 9 chickens) as you work your way up, making each vertical column (from left to right, Gift, horses, cows, etc.... essientially, once you line up your equations, each column represents a variable) have only a single one and nothing else but zeroes, thorough division of the given row, or additon of multiples of rows above or below, you end up arriving at the same answer: 1 gift = 200 chickens.

This is a bit moot because there are only about two variables per line, but once you add 3 or 4 variables per row, this method makes it much quicker to solve rather than trying to get z=t-4s+3u, and then substituting the (t-4s+3u) for each instance of z in other equations, contnuing until one variable solves, and then working backwards.

It may happen that the problem you are solving has no soluton. This will become apparent through matrices if one row in your coefficient matrix has only 0 entries, but results in a non-0 vector, or vice versa, you have coefficient of 1, but a vector of 0.

I know that this is a bit over your head, but look into it, ask your teachers, or anyone else and see if they can help you out. Matrices end up being a helpful tool in computer programming, specifically, image processing. If you care at all, fighter jets use matrix processing to assist the pilot in targetting.

Below, I have drawn for you your initial augmented matrix. The left side represents the coefficient matrix, and the right side your vector matrix (the number of chickens you need to get each variable)


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by the by, if you ARE curious and want to know more, you can message me and we can set something up.