[ 數學 ]雞兔同籠

設兔有y隻，則雞有(100-y)隻
4y+2(100-y)=316
4y+200-2y=316
4y-2y=316-200
2y=116
y=116除2(約簡)
y=58
答:兔有58隻，雞有100-58=42隻

Let the number of the chicken be X , the number of the rabbits be Y

X+Y= 35 --------- (1)
2X+4Y= 94 -------(2)

(1) X 2

2X+2Y = 70 --------(3)

(2) - (3)

(2X-2X) + (4Y-2Y) = 94 - 70
2Y = 24
Y = 12
Sub Y = 12 into (1)

X+12 = 35
X = 23

So the number of the chicken and the rabbits are 23 and 12 respectively.
(please used three dots to represent 'so' and you should know it)

This is the method of elimination.

I don't use the method of substitution to caculate it because it is more complicated. I hope that I can help you.

2010-01-06 17:58:48 補充：
Oh, sorry that the method of substitution is also easy to caculate you can either choose the method from jasmin_1110 or from me. It's also correct. This just depends on what method do you want to use.

兔=(94－2*35)/(4－2)=12
雞=35－12=23

雞=X
兔=Y

X+Y=35...........(1)
2X+4Y=94........(2)

(1)
X=35-Y

IF X=35-Y,
(2)
2(35-Y)+4Y=94
70-2Y+4Y=94
2Y=24
Y=12

Y=12
(1)
X+12=35
X=23

SO 雞23隻, 兔12隻