數學題 急

1. 假設該部相機的來價為 x 元.

標價比來價高30%, 標價 = x * (1 + 30%) = x * 1.3 = 1.3x
以八折出售, 售價 = 標價 * 80% = 1.3x * 0.8 = 1.04x
盈利 = 售價 - 來價
=> 200 = 1.04x - x
=> 200 = 0.04x
=> x = 200 / 0.04 = 5000

部相機的來價為 5,000 元.
標價 = 1.3x = 1.3 * 5000 = 6,500 元.
售價 = 1.04x = 1.04 * 5000 = 5,200 元.


2. 假設該貨品的來價為 y 元.

標價比來價高20%, 標價 = y * (1 + 20%) = y * 1.2 = 1.2y
售價 = 來價 + 盈利 = y + y * 8% = (1 + 0.08) * y = 1.08y
以七五折出售, 售價 = 新標價 * 75%
=> 新標價 = 售價 / 75% = 1.08y / 0.75 = 1.44y
=> 新標價比舊標價高 1.44 - 1.20 / 1.20 = 0.2 = 20%, i.e. 百分之 二十.

1. 設一部相機來價為 n,
n x (1+30%) x (1-20%) - n =200
n x 1.3 x 0.8 - n =200
0.04n = 200
n = 5000

來價= $5000
標價= 5000x1.3 = $6500
售價= 6500x0.8 = $5200


2. 某百貨公司貨品來價為 n, 設該公司應把標價提高百分之幾為k,
n x (1+k%) x (1-25%) = n x (1+8%)
(1+k%) = 1.44
k=44%
所以，該公司應把標價提高百分之44