匿名
匿名 發問於 科學及數學數學 · 1 十年 前

Maths 問題

Question:

A housewife pays $75 for some apples. If the price of each apple is redued by $0.5, she can buy 5 more apples with the same amount of money. Find the original price of an apple.

我想到條式如下:

Let x be the price of original price of an apple

75/x = (75/x-1) -5

但我不知道 (75/x -1) -5 應如何計,

pls. help, 請列式.

更新:

sorry, typing error, it should be (75/x-0.5)-5

更新 2:

我想問吓

(2x-1)/2 是不是由 x - 1/2 通分母而來?

x 變成分數, 應是 x/x or x/1?

2 個解答

評分
  • wy
    Lv 7
    1 十年 前
    最佳解答

    Let x be the original price of an apple.

    Therefore, no. of apples he can buy = 75/x.

    When the price is decreased by 0.5, new price is (x - 0.5).

    No. of apples he can buy = 75/(x - 1/2). Therefore the equation is:

    75/(x - 1/2) - 5 = 75/x

    75/[2x -1)/2] - 5 = 75/x

    150/(2x - 1) - 5 = 75/x. Multiply all terms by x(2x-1), we get

    150x - 5x(2x-1) = 75(2x - 1)

    150x - 10x^2 + 5 = 150x - 75

    10x^2 = 75 + 5 = 80

    x^2 = 8

    x = sqrt8 = 2sqrt2.

    2008-08-19 21:31:04 補充:

    Correction: Line 9 should be 150x - 10x^2 + 5x = 150x - 75, that is 10x^2 -5x - 75 = 0,

    2x^2 - x - 15 = 0, (2x + 5)(x - 3) = 0. So x = -5/2(rej.) and x = 3. So original price is $3.

  • 1 十年 前

    A housewife pays $75 for some apples. If the price of each apple is redued by $0.5, she can buy 5 more apples with the same amount of money. Find the original price of an apple.

    Let x be the price of original price of an apple

    75/x = 75/(x-0.5) -5

    2x2 - x - 15 = 0

    (2x+5)(x-3) = 0

    x = 3

    the price of original price of an apple is $3

    資料來源: me
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