F.1 Mathz 2題

*1
Last month, there were 30 male students and 20 female students in the chess class. The number of male students decreases by r% and the number of female students increases by r% in this month. If the number of male and female students are the same in this month,find r.

This month, number of male students = number of female students
30(1 - r%) = 20(1 + r%)
30 - 0.3r = 20 + 0.2r
0.5r = 10
r = 20


*2
Two shops sell the same brand of chocolate at the same price.Today they both cut down its price. Shop A lowers the price by 30%, and increases by30% afther a week. Likewise, shop B lowers its price by 40%, and increases by 40% afther a week. Are the prices of the chocolate at the two shops still the same afther a week?

Let $P be the original price.

After a weak:

Price of the chocolate at shop A
= $P(1 - 30%)(1 + 30%)
= $P(0.7)(1.3)
= $0.91P

Price of the chocolate at shop B
= $P(1 - 40%)(1 + 40%)
= $P(0.6)(1.4)
= $0.84

The prices of the chocolate at the two shops are not the same after a week.