Variation - Ans.fyi 參考答案

Variation

2011-02-20 3:01 am

Let the unit cost of a certain toy be $C when n pieces of the toy are produced, and C varies inversely the square root of n. It is given that when 100 pieces of the toy are produced, the unit cost is $50. If the unit cost of toy decreases by 20%, by what percentage does the quantity of toys produced increase?

回答 (1)

知識就是力量

2011-02-20 5:09 am

✔ 最佳答案

C = k/√n, where k is a non-zero constant.
Put n = 100 and C = 50
50 = k/√100
k = 500
So C = 500/√n
By making n as the subj., i.e. n = 250000/C^2
Let $C_0 and n_0 be the original cost and quanitity produced.
New cost = C_0 (1 - 20%) = 0.8C_0
New quanitity produced
= 250000/(0.8C_0)^2
= 250000/0.64(C_0)^2
= 1.5625n_0
Percentage change
= (1.5625n_0 - n_0) / n_0 * 100%
= 56.25%
The quantity increases by 56.25%

2011-02-19 21:09:56 補充：
New cost = C_0 (1 - 20%) = $0.8C_0
I miss out the $ sign

2011-02-21 19:02:40 補充：
I wonder if my answer is correct. Please don't hesitate to tell me if wrong.

參考: Knowledge is power.

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