# 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.

Let x be the price of original price of an apple

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

pls. help, 請列式.

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

(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

• 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.

• 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