Thursday

October 2, 2014

October 2, 2014

Posted by **Max** on Tuesday, February 15, 2011 at 12:18am.

- math -
**Reiny**, Tuesday, February 15, 2011 at 12:48amDon't you just love these 19th Century textbooks?

A pig for $3 !!!!! WOW

let number of cows be x

let the number of pigs be y

then the number of chickens = 100-x-y

10x + 3y + .5(100-x-y) < 100

times 2

20x + 6y + 100 - x - y < 200

19x + 5y < 100

consider 19x + 5y = 100

But , what is the question?

Do you want the different combinations you can buy? Do we want as close as possible to $100?

Remember x and y have to be positive integers.

so x has to be between 1 and 5

form a table with columns

x, y, and 100-x-y, and cost

1 16 83 99.50

1 15 82 86.00

...

5 1 94 100

x=5, y=1 is the only combination that will use all the money

He should buy 5 cows, 1 pig and 94 chickens

5+1+94 = 100

$50 + $3 + $47 = $100

- math -
**tchrwill**, Tuesday, February 15, 2011 at 8:25amA Golden Oldie

If you had a $100.00 to spend and need to buy a 100 animals, and cows cost

$10.00, pigs $3.00, chickens .50 cents each,how many of each can you buy?

Let C, P, and F be the numbers of cows, pigs, and fowl.

1--C + P + F = 100

2--10C + 3P + .5F = 100 or 100C + 30P + 5F = 1000

3--Multiplying (1) by 5 and subtracting from (2) yields 19C + 5P = 100

4--Dividing through by 5 gives P + 3C + 4C/5 = 20

5--4C/5 must be an integer as must be C/5

6--Let C/5 = k making C = 5k

7--Substituting (6) back into (3) gives 95k + 5P = 100 making P = 20 - 19k

8--k can only be 1 making C = 5, P = 1, and F = 94

Check: 10(5) + 3(1) + .5(94) = $100

Alternatively

Let C, P, and F be the numbers of cows, pigs, and fowl.

1--C + P + F = 100

2--10C + 3P + .5F = 100 or 100C + 30P + 5F = 1000

3--Multiplying (1) by 5 and subtracting from (2) yields 19C + 5P = 100

4--Solving for P, P = 20 - 19C/5

5--19C/5 must be an integer meaning that C must be evenly divisible by 5.

6--Thus, C must be 5 making P = 1, C = 5, and F = 94.

**Answer this Question**

**Related Questions**

avd. math - farmer joe needs cows pigs an chickens cows cost 10.00 each and pigs...

Math - I have $100.00 dollars to spend to buy 100 animals. Cows cost $50.00 each...

math - i have 100.00 to spend on 100 animals. the chickens are .05 each, the ...

Math - a horse is $5 a cow is $3 & chickens r $.50 ea. now buy 100 animals 4 ...

math - a farmer bought chickens, goats and sheep. He bought 100 animals and ...

math - A farmer has $100.he has to buy 100 farm animals.He has to spend exactly...

maths - I need to buy 100 farm animals with $100.. I need to have brought at ...

math - I have 50.00 to buy 50 animals. Chickens are .50, cows are 2.50,and birds...

math - Afarmer must purchase 100 animals. He must spend exactly $100. He must ...

Math - John had some animals. One-fourth were horses, one-half were cows, and ...