中二數學題...二元一次方程

2008-01-21 2:16 am

1.解以下聯合方程.
72 - 2m + n = 6m + 7n = 3m + 8n - 25

2.何先生買入一批可樂糖和蘋果糖,共重80分斤,而可樂糖和蘋果糖的成本價分別是每公斤$40和$50.他把兩種糖混合,並以每公斤$70的價錢售出,獲利60%.
(a)要求他買入該批糖果的總成本。
(b)他買入每種糖果多少公斤?

3.若二元一次方程 4x + 3y + c = 0 的圖像通過原點,則c=?
a.-3 b.0 c.3 d.4

4.一幅元朗的街道圖的比例尺為1:10000.在該圖中,元朗邨的長度
和闊度分別是1.8cm和1.1cm.求元朗邨的實際面積.
答案係198m^2定19800m^2?

回答 (1)

A.T.

2008-01-21 2:35 am

✔ 最佳答案

1.
72-2m+n = 6m+7n ------------- (1)
6m+7n = 3m+8n-25 ------------(2)

from (2)
3m = n-25
n = 3m+25 -------(3)

sub (3) into (1)
72 - 2m + 3m+25 = 6m+ 21m + 175
m = 27m+ 78
m = 78/(-26)
m = -3 ------------(4)

sub (4) to (3)
n = 3(-3) +25 = 16

m = -3 , n = 16

2.
(a) 獲利 60%
每公斤成本 = $70 / 160% = $43.75
總成本 = 80 分斤 x $43.75 = $3500

(b)
Let x be 可樂糖, then let y be 蘋果糖
x + y = 80 ------------------(1)
40x + 50y = 3500 ---> 4x + 5y = 350--------------(2)

from (1)
x = 80-y ----------(3)

sub (3) into (2)
4(80-y) + 5y = 350
320- 4y + 5y = 350
y = 30 ----------(4)

sub (4) into (3)
x = 80- 30
x = 50

50公斤可樂糖及 30公斤蘋果糖

3. c = 0
answer = b
becoz 通過原點的話 when x = 0, y = 0
c must be 0

4. (1.8x10000)/100 x (1.1x10000)/100
= 19800m^2

參考: me

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