數學equation qs & % qs

👨🏻‍🏫 學術台數學

[匿名]

2008-08-27 1:56 am

問題一：Ann had a bag of glass beads.She used half of the beads to make a necklace.She and her sister than use 1/6 and 1/7 of the beads respectively to make two bracelets.If there are 16 glass beads left, find the original number of glass beads.

問題二：If the two adjaccent sides of a square measure x cm and (2x-3)cm respectively,find the perimeter of the square.

問題三：last month,there were 30male students and 20 female students in the chess club.The number of male students decreases by r% and the number of female students increases by r% in this month.If the number of the male and female students are the same in this month,find r.

問題四：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 by 30%,and increases by30% after a week.Likewise,shop B lower its price by 40%,and increasas by 40% after a week.Are the price of the chocolate at the two shops still the same after a week?

更新1:

第1同2題用equation！第3同4既用percentage！！

回答 (2)

擺明大你

2008-08-27 2:23 am

✔ 最佳答案

Q1.)
Let Y be the original number of glass beads
Y x (1 - 1/2 - 1/6 - 1/7) = 16
Y x [(42 - 21 - 7 - 6) / 42] = 16
Y x [8 / 42] = 16
Y = 84
Therefore, the original number of glass beads is 84

Q2.)
2x - 3 = x
x = 3
The perimeter of the square = 3 x 4 = 12cm

Q3.)
30(1 - r%) = 20(1 + r%)
30 - 30 x 0.01r = 20 + 20 x 0.01r
10 - 0.3r = 0.2r
0.5r = 10
r = 20

Q4.)
Let Y be the original price of the chocolate
Shop A:
Y(1 - 30%)(1 + 30%)
= Y(0.7)(1.3)
= 0.91Y
Shop B:
Y(1 - 40%)(1 + 40%)
= Y(0.6)(1.4)
= 0.84Y

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

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Uncle Michael

2008-08-27 2:21 am

問題一：
Let n be the original number of glass beads.

n - (1/2)n - (1/6)n - (1/7) = 16
(42/42)n - (21/42)n - (7/42)n - (6/42) = 16
(8/42)n = 16
n = 16(42/8)
n = 84

Ans: The original number of glass beads = 84

=====
問題二：
All sides of squares are equal in length.
x = 2x - 3
x = 3

Length of each side of the square = 3 cm

Perimeter of the square = 3 cm x 4
Perimeter of the square = 12 cm

=====
問題三：
30(100 - r)% = 20(100 + r)%
3(100 - r) = 2(100 + r)
300 - 3r = 200 + 2r
5r = 100
r = 20

=====
問題四：
Let $P the original price of the chocolate.

Price of the chocolate at shop A after a week = $P x (100 + 30)% x (100 - 30)%
Price of the chocolate at shop A after a week = $0.91P

Price of the chocolate at shop B after a week = $P x (100 + 40)% x (100 - 40)%
Price of the chocolate at shop A after a week = $0.84P

Hence, their prices are different after a weak.
=

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