So you think you're good at math ....... lets see if you can answer this right !?

Question

Your boss has given you 100 dollars to go buy some chickens from the farmer down the road.your boss tells you he wants you to spend the whole 100 dollars and bring back 100 chickens no more no less he also said that you must buy at least 1rooster, 1hen & 1baby chick.... when you arrive at the chicken farm you see a sign that has roosters 5dollars each hens 1dollar each baby chicks 5cents each now how many of each do you have to buy to spend the 100 dollars and bring your boss back 100 chickens? ( remember you must buy at least 1 of each )

this is not a trick question it can be done

Answer 1

80 chicks
19 roosters
1 hen

x = rooster
y = chick

x + y = 5x + .05y
.95y = 4x
95Y = 400x
19y = 80x

therefore there would be 19 roosters and 80 chicks

Answer 2

Let
r = roosters
h = hens
c = chicks

There are only 2 equations (even though there are 3 variables, which means that there is a possibility that there are more than one solution.)
r + h + c = 100
5r + h + 0.05c = 100

Subtract the 2nd equation from the first equation
-4r + 0.95c = 0

Transposs
4r = 0.95c

Divide
r = 0.95/4 c

Multiply 2/2 to the right side
r = 1.9/8 c

Multiply 10/10 to the right side
r = 19/80 c

We know that c must be between 0 and 100, and if c has any value other than 80, then r will not be a whole number, which is impossible. Thus, c = 80. r is:
r = 19/80 (80)
r = 19

Get the value of h
r + h + c = 100
h = 100 - r - c
h = 100 - 19 - 80
h = 1

Therefore, you must buy 19 roosters, 1 hen and 80 baby chicks.

19 roosters != $ 95
1 hen != $ 1
80 baby chicks != $ 4
100 chickens != $100

^_^

Answer 3

You must buy chicks in increments of 20, so there's only 4 possible numbers for the chicks, 20, 40, 60, 80. Use process of elimination. If you buy 20 chicks, that means you have 99 dollars to spend, purchase roosters because chickens + dollars > 100, 21 chickens 94 dolalrs, 22 chickens 89 dollars, 23 chickens 84 dollars, 24 chickens 79 dollars, 25 chickens 74 dollars.

Uh oh, now that chickens + dollars < 100, buy 20 more chicks. 45 chickens, 73 dollars. Now go back to roosters, 46 chickens 68 dollars, 47 chickens 63 dollars, 48 chickens 52 dollars. Chickens + dollars = 100, now you buy 52 hens.

40 chicks, 52 hens, and 8 roosters = 100.
(8*5) +52 + (40*.05) = $100

I'm sure there's a way to do it algebraically but I didn't feel like pondering it.

Addendum : WOW, did I screw that one up!!! Just goes to show you're better off doing the algebra. You all can ignore my rambling response now, least I can admit when I'm wrong. :p

This solution probably would have worked better if I realized 63 - 5 <> 52 LOL

Answer 4

You buy x roosters, y hens and z chicks,
where x + y + z = 100
and 5x + y + .05z = 100

The second equation is equivalent to
100x + 20y +z = 2000, and subtracting the first from it gives
99x + 19y = 1900

The positive integer solutions to this are x = 19, y = 1, and so you must buy 19 roosters ($95), 1 hen ($1) and 80 chicks ($4).

Answer 5

Let,
R = # of Roosters
H = # of hens
C = # of Chicks
(R, H, and C must be positive integers,each less than 99)

R + H + C = 100----------Eq1------Total 100 Chickens
5R +1H +0.5C = 100-----Eq2-----Must spend $100

(Eq1 minus Eq2) gives you:
-4R+0.95C = 0
That is,
R = (0.95/4)C

Trying different integer values of C and looking for resulting integer value of R will result in the following acceptable answer:

for C = 80, R will 19.... (the only set of values for which all conditions will be met).

Hence H must be 1

So, the answer is:

19 Rosters, 1 Hen, and 80 Chicks.

Answer 6

let number of hens u wana buy be X
'' of rosters be Y
and " of baby chicks be Z
money you gona spend on hens = 1.X
money u gona spend on rooster 5Y
money on chicks 0.5Z
1.X + .05 Z + 5Y = 100
now if we were to make any two of it 1 then the other variable left should divide to give a whole number( u need full chiken)
so let X,Y be 1(coz if you divide any nmber by a decimal number you will get a whole number)
so 1 + 5+0.5Z= 100
0.5Z = 100- 6
Z= 94/.5=
do your maths

Answer 7

19 rooseters, 1 hen and 80 baby chicks.

19+1+80=100
19*5+1+80*0.05=100

Answer 8

Dudette, I'm sure you're probably very bright [or you wouldn't have posted that question], but I passed maths by 90% in College, a full 9% above the next highest student and I'm not spendin half an hour [I said I was bright, not fast] doing that puzzle. Now will ya get to College.......... [Ps, College is easier in the UK as the gov pays *all* bills as we do it, so don't try to pass by that mark; just pass comfortably [that's all I was trying for anyhows, but it's as easy to do something right as wrong]]

Answer 9

r - roosters
h - hen
c - baby chicken

then
5r + h + (5/100)c = 100
or 500r + 100h + 5c = 10000 --- 1

also
r + h + c = 100
or 100r + 100h + 100c = 10000 --- 2

comparing 1 and 2,

500r + 5c = 100r + 100c
or 400r = 95c
or 80r = 19c

The only soln to this eq keeping r and c < 100 and integrs is
r = 19 and c = 80
so, h = 100 - 80 - 19 = 1

so u buy
r -- 19
h -- 1
c -- 80

Check amount yourself... it comes to $100

Answer 10

19 roosters and one hen is going to mean one sore cnut for the hen.