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,

爸爸的年紀將是言雅的2倍!(請用聯立方程計算)

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?

Explain your answer.

2 Answers

Rating
  • 6 years ago
    Favorite Answer

    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?!?!

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