中二數學~不懂怎樣計這3題

1 let two numbers x,y
x+y=94...(1)
x-y=14...(2)
so
2x=108
x=54
y=40
2
let two numbers x,y
x+y=73...(1)
x-y=7...(2)
so
2x=80
x=40
y=33
3
let the price of pen x , pencil y
10x+4y=78...(1)
18y+6x=78..(2)
10x+4y=18y+6x
4x=14y
x=3.5y
so
10(3.5y)+4y=78
39y=78
y=2
x=7
the price of pen 7 , pencil 2


2007-02-08 15:36:44 補充：
補充difference 解兩者之差第一,二條我設x>y所以x-y是正數﹐符合到題目要求

1. The sum of two numbers is 94 and their difference is 14. Find the numbers.

Set the bigger’s number to be x and the smaller’s number to be y :
x + y = 94, then x = 94 - y
x – y = 14, then x = 14 + y
94 – y = 14 + y
94 – 14 = y + y
2y = 80
y = 40
x = 94 – y
x = 94 – 40
x = 54



2. Find two numbers whose sum is 73 and whose difference is 7 .( whose difference )

呢條問題的解釋係找出兩個數目佢地的和是73及佢地的差係7。
Set the two numbers to be x and y :
x + y = 73, then x = 73 - y
x – y = 7, then x = 7 + y
73 – y = 7 + y
73 – 7 = y + y
2y = 70
y = 35
x = 73 – y
x = 73 – 35
x = 38



3. Either 10 pens and 4 pencils or 18 pencils and 6 pens can be bought for $78, what is the price of each ?

Set the price of the pen is x and the price of the pencil is y :
10x + 4y = 78, then 10x = 78 – 4y, then x = (78 – 4y) / 10
18y + 6x = 78, then 6x = 78 – 18y, then x = (78 – 18y) / 6
(78 – 4y) / 10 = (78 – 18y) / 6
(78 – 4y) x 6 = (78 – 18y) x 10
468 – 24y = 780 – 180y
– 24y + 180y = 780 - 468
156y = 312
y = 2
x = (78 – 4y) / 10
x = (78 – 4(2)) / 10
x = 70 / 10
x = 7

1) Let the two numbers are x and y.
x + y = 94
=> x = 94-y

x - y = 14
=> (94-y) - y = 14
=> 94-2y = 14
=> 2y = 94-14
=> y = 80/2
=> y = 40
x= 94-40 = 54

2) whose difference = 它们的差
计法同上题.

3) 10 pens and 4 pencils can be bought for $78
即是 sum of 10 pens and 4 pencils = $78
18 pencils and 6 pens can be bought for $78
即是 sum of 18 pencils and 6 pens = $78

Let price of pen be x
Let price of pencil be y

10x + 4y = 78
18y + 6x = 78

其余计法同第一题.