P2-6.某養夫飼養了一批雞和兔。若雞比兔多5隻,但兔腳的總數比雞腳的總數多40,求兔的數目
Let x be the no. of chickens, y be the no. of rabbits
x = y + 5 ------ (1)
4x – 2y = 40 ----- (2)
Subs. (1) into (2):
4(y+5) – 2y = 40
4y + 20 – 2y = 40
2y = 20
y = 10
x = 15
P55-4(A)
設2a=3b=5c。求a:b:c-答案我有..我想知點解點計
可先將其拆為二式
2a = 3b ----- (1)
3b = 5c ----- (2)
From (1):
a/3 = b/2
a : b = 3 : 2 = 15 : 10
From (2):
b/5 = c/3
b : c = 5 : 3 = 10 : 6
a : b : c = 15 : 10 : 6
p55-5
若3a=2b=5c,則求1/a:1/b:1/c(1over A:1over B:1over C)
3a = 2b
1/a : 1/b = 3 : 2
2b = 5c
1/b : 1/c = 2 : 5
1/a : 1/b : 1/c = 3 : 2 : 5
P55-6
若x+1:x-1=1:2
求5x+3的值
x+1 : x-1 = 1 : 2
(x+1)/1 = (x-1)/2
2(x+1) = (x-1)
2x + 2 = x – 1
x = -3
已知x:y+1=4:5
(a)以y表示x
(b)若2x=9y=97,求x及y的值。
x : y+1 = 4 : 5
x/4 = (y+1)/5
x = 4(y+1)/5
(不知道題目有沒有打錯)
2x = 97
x = 97/2
9y = 97
y = 97/9
p56-5
若y是兩部分的和,一部分隨x而正變,另一部分隨x而反變。當x=1時,y=5。當x=6時,y=12.5。
(a)求x和y的關係。
y = ax + b/x
For x=1, y=5,
5 = a + b ----- (1)
For x=6, y=12.5
12.5 = 6a + b/6 ----- (2)
From (1):
a = 5 – b ----- (3)
Subs (3) into (2):
12.5 = 6(5-b) + b/6
75 = 36(5-b) + b
75 = 180 – 36b + b
35b = 105
b = 3
a = 2
y = 2x + 3/x
y=4x+3x^2
以x表示y...
y = 4x + 3x2
y/3 = x2 + 4x/3
y/3 + (2/3)2 = x2 + 4x/3 + (2/3)2
y/3 + 4/9 = (x+2/3)2
3y + 4 = (3x+2)2
(3y+4)1/2 = 3x + 2
3x = (3y+4)1/2 – 2
x = [(3y+4)1/2 – 2 ]/3
