率與比(form2數學)

1.
假設最小的數是3x, 這三個數字是3x, 4x 及 5x
5x - 3x = 2x = 10
x = 5
這三個數字是15, 20 及 25

2.
a:c = 1:2 = 3:6
b:a = 2:3
a:b:c = 3:2:6

3.
(2x - y): (2x + y) = 3:7
14x - 7y = 6x + 3y
8x = 10y
x:y = 10:8

4.
a:b = 3:2 = 9:6
b:c = 3:4 = 6:8
a:b:c = 9:6:8

1. 3:4:5=6:8:10=9:12:15=12:16:20=15:20:25
25-15=10
這三個數=15,20,25
2. a : b : c = c : a : b
1 2 2 1
3 2 3 2 = 6:3:2
a:b:c=3:2:6
3. 2x-y=3 .......(1)
2x+y=7.......(2)
(1),2x-y=3
y=2x-3...........(3)
(3)to(2), 2x+(2x-3)=7
2x+2x-3=7
4x=10
x=2.5
x=2.5to(1), 2(2.5)-y=3
5-y=3
y=2
x=2.5,y=2
x:y=2.5:2=5:4
4. a : b : c
3 2
3 4
__________
9 : 6 : 8
a:b:c =9 : 6 : 8

設二個正數為3x,4x,5x
因為5x-3x=10
所以x=5
則那三個正數為15,20,25
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b:a=2:3
a:c=1:2=3:6
a:b:c=3:2:6
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(2x+y)*3=(2x-y)*7
6x+3y=14x-7y
8x-10y=0
x:y=10:8=5:4
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a:b=3:2=9:6
b:c=3:4=6:8
a:b:c=9:6:8