4條f.2升f.3數學~~(率和比)!!

1.
4x - 5y = 0
4x = 5y
x/5 = y/4

設x/5 = y/4 = k
所以 x = 5k 及 y = 4k

(3x - y) : (2x + 3y)
= (3*5k - 4k) : (2*5k + 3*4k)
= 11k : 22k
= 1 : 2


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2.
a : b = 8 : 12
b : c = 12 : 15
所以 a : b : c = 8 : 12 : 15

設 a = 8k, b = 12k, c = 15k

(3a - b) : (b + 2c)
= (3*8k - 12k) : (12k + 2*15k)
= 12k : 42k
= 2 : 7


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3.
2x = 3y = 4z
2x/12 = 3y/12 = 4z/12
x/6 = y/4 = z/3

設x/6 = y/4 = z/3 = k
則 x = 6k, y = 4k, z = 3k

(x - y + z) : (x + y - z)
= (6k - 4k + 3k) : (6k + 4k - 3y)
= 5k : 7k
= 5 : 7


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4.
a : b = 9 : 15
b : c = 15 : 10
所以 a : b : c = 9 : 15 : 10

設 a = 9k, b = 15k, c = 10k
(2a + 3b - c) / (3a - 2b + c)
= (2*9k + 3*15k - 10k) / (3*9k - 2*15k + 10k)
= 53k / 7k
= 53 / 7