F.3 Maths(Percentage)

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知識就是力量

2008-10-14 1:31 am

Two containers A and B contain two solutions respectively, which are mixtures of alcohol and water. New mixtures P and Q are produced by mixing the solutions in containers A and B in the ratio 3 : 2 and 1 : 2 respectively. If P and Q contain 40% and 32% alcohol respectively, find the percentage of alcohol in containers A and B respectively.

更新1:

To: ai_kawah, your ans is incorrect. To: eelyw How come you can get P = 3a/5 + 2b/5 = 0.4 ? Why do we need to over 5 in this case? Also, and how come you can get Q = a/3 + 2b/3 = 0.32 Why do we need to over 3 in this case?

回答 (2)

用戶10012

2008-10-14 1:56 am

✔ 最佳答案

Let the % of alcohol in A be a, and in B be b.
Amount of alcohol in P = 3a/5 + 2b/5 = 0.4
That is 3a + 2b = 2....................(1)
Amount of alcohol in Q = a/3 + 2b/3 = 0.32
a + 2b = 0.96......................(2).
(1) - (2) we get
2a = 1.04
a = 0.52 = 52%.
From (1)
(3)(0.52) + 2b = 2
1.56 + 2b = 2
2b = 0.44
b = 0.22 = 22%.

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[匿名]

2008-10-14 1:55 am

3A+2B = 0.4x

A+2B = 0.32x
=> A = 0.32x -2B

3(0.32x-2B) = 0.4x
=> 0.96x - 6B = 0.4x
=> 0.56x = 6B
=> B = 0.56x / 6 = 0.093x

Container B = 9.3% alcohol

A = 0.32x - 2 (0.093x)
A = 0.13x

Container A = 13% alcohol

參考: CLOUDWAH

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