Man fu asked in 科學及數學數學 · 6 years ago

# 中二數學問題三條!20點!要詳細步驟!

14.) Among the participants in a singing contest,the numbers of boys and girls

are in the ratioo3:5.It is given that the number of boys and girls are in the ratio

3:5.It is given that the number of boys is 22 less than that of girls.

(a)Find the total the number of participartpants in the singing contest.

(b)If 4 boys and 4 girls quit the contest,does the ratio of the numbers of boys

and girls remain unchanged?Explain you answer.

15.)爸爸現在的年紀是言雅的7倍,10年後是言雅的3倍。從現在起多少年後,

19.)Lorry I travels from A to B with a uniform speed of a km/h.Lorry II travels from B to A with a uniform speed 20% higher than that of LorryI.The two lorries start

at the same time,and meet after b hour(s).

(a)Let L km be the distance between A and B.Express L in terms of a and b,andsimplify the formula obtained.

(b)Change the subject of the formula obtained in (a) to b.

(c)If the two lorries meet after 2.5h,can lorry I complete the journey in 5 h?

Rating
• 6 years ago

14.

a)

Let b be the number of boys

b/b+22=3/5

b=33

Total number of participants=33+33+22=88

b)

NO

new ratio=(33-4):(33+22-4)

=29:51

15

假設今年爸爸x歳,言雅y歳

x=7y---(1)

10+x=3(10+y)

x=20+3y---(2)

Put (1) into (2)

7y=20+3y

y=5

今年言雅5歳,爸爸35歳

假設r年後爸爸的年紀是言雅的2倍

35+r=2(5+r)

r=25

所以25年後爸爸的年紀是言雅的2倍

19

a)

L=ab+(1+20%)ab

=2.2ab

b)

L=2.2ab

b=L/2.2a

c)

No

if they meet after 2.5 hour,

distance(L km) = (2.2a)2.5 = 5.5a km

so,lorry I complete the journey in 5.5 h

Source(s): me
• 6 years ago

我已解答，但被指違規：

請看我的答案：

http://postimg.org/image/k39nyc6tz/

2014-02-05 14:34:15 補充：

Man fu，我己經 send 了 email 給你，請看看。

2014-02-05 14:35:21 補充：

14)

(a) Let the number of boys be 3k and number of girls be 5k where k is a constant.

3k = 5k - 22

2k = 22

k = 11

The number of boys is 3k = 33

The number of girls is 5k = 55

The total number of participants in the singing contest is 33 + 55 = 88.

2014-02-05 14:35:30 補充：

(b) If 4 boys and 4 girls quit the contest, there are

33 - 4 = 29 boys and

55 - 4 = 51 girls.

The ratio is 29 : 51 which is different from 3 : 5.

Therefore, the ratio of the numbers of boys and girls does NOT remain unchanged.

2014-02-05 14:35:53 補充：

15) 設 x 為爸爸現在的年紀, y 為言雅現在的年紀。

{x = 7y

{x + 10 = 3(y + 10)

7y + 10 = 3(y + 10)

7y + 10 = 3y + 30

4y = 20

y = 5

x = 7y = 35

爸爸現在的年紀是 35 歲。

言雅現在的年紀是 5 歲。

設現在起 n 年後, 爸爸的年紀將是言雅的2倍。

35 + n = 2(5 + n)

35 + n = 10 + 2n

n = 25

所以, 現在起 25 年後, 爸爸的年紀將是言雅的2倍。

2014-02-05 14:36:21 補充：

19)

(a) The speed of Lorry 2 is 1.2a km/h.

In b hours, both lorries travel in total L km.

Therefore, a × b + 1.2a × b = L

(a + 1.2a) × b = L

(2.2a) × b = L

L = 2.2ab

2014-02-05 14:36:35 補充：

(b) L = 2.2ab

b = L/(2.2a)

2014-02-05 14:37:05 補充：

(c) Given that b = 2.5.

2.5 = L/(2.2a)

L = 2.5 × 2.2a = 5.5a

The time Lorry I takes to complete the journey is

Distance / Speed

= L / a

= 5.5a / a

= 5.5 hours

Therefore, Lorry I cannot complete the journey in 5 hours.

2014-02-05 14:37:41 補充：

奇怪！　完全不知道哪裏違規？！？！