方程！～急！～

籠中有些小雞和小兔。1/3小免只有３隻腳。如果頭的總數是35個而腳的總數是90隻。求:
a.小雞的數目 b.有４隻腳的小兔的數目

設小雞的數目係a
設小兔的數目係b

a + b = 35
b = 35 - a
2a + 3(1/3b) + 4(2/3b) = 90…….(i)
Put b =35 - a into (i), we get
2a + 3[1/3(35 - a)] + 4[2/3(35 - a)] = 90
2a * 3 + 3[1/3(35 - a)] * 3 + 4[2/3(35 - a)] * 3 = 90 * 3
6a + 105 - 3a + 280 - 8a = 270
385 - 5a = 270
385 - 270 = 5a
23 = a
a = 23(=小雞的數目)

therefore, b = 35 - a = 35 - 23 = 12
1/3b = 12 * 1/3 = 4
2/3b = 12 * 2/3 = 8 (=有４隻腳的小兔的數目)

ans. a.小雞的數目係23隻
b.有４隻腳的小兔的數目係8隻

設小雞有y隻, 小兔有x隻
(3x/3) + [4(2x)/3] + 2y = 90 -------- (1)
x + y = 35 ------------------------------- (2)
From (1),
(3x/3) + (8x/3) + 2y = 90
(11x/3) + 2y = 90
11x + 6y = 270 ---------- (3)
From (2),
x = 35-y--------------------- (4)
sub (4) into (3),
11(35-y) + 6y = 270
385 - 11y + 6y = 270
-5y = -115
y = 23
sub y = 23 into (4),
x = 35 - 23 = 12
∴小雞有23隻, 小兔有12隻.
有４隻腳的小兔的數目
= 12 (2/3)
= 8(隻)

哇!!!!!!!!!!!!!!!!!!!!!!!!!!!!