Maths 問題

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