Anonymous
Anonymous asked in 科學及數學數學 · 1 decade ago

Variations HELP (15 points)!!!! HELP!!

1.The monthly expense $E in staff salary in a junior grade is directly proportional to the number of staff (n). The expense is $18,000 for 3 staff.

(a) Find the expense when there are 4 staff in the grade.

(b) Find the number of staff in the grade when the, monthly expense is $54,000.

2. The value of a car $C varies inversely as the number of years n for which it has been used. If the value of a car in the year 2004 after it has been used for 2 years is $25,000.

(a) express C in terms of n.

(b) find the value of the car in the year 2007.

3.The average cost(per head) of providing a school lunch is partly constant and partly varies inversely as the number of students taking the lunch. When 144 students take lunch, the average cost is $17. The average cost becomes $16 when the number of students rises to 168.

(a.) Find an equation connecting the average cost (per head) and the number of students taking lunch.

(b.) How many students would be required to reduce the cost of lunch to $14?

(c.) If 1000 students would take lunch, a rebate of $500 would be given to the school. Calculate the actual average cost per head.

with 簡單中文解題pls!!! thanks!!

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  • 1 decade ago
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    1.The monthly expense $E in staff salary in a junior grade is directlyproportional to the number of staff (n). The expense is $18,000 for 3staff.

    Ans:

    let E=kn

    The expense is $18,000 for 3staff

    =>18000=k(3)

    =>k=6000

    so E=6000n

    (a) Find the expense when there are 4 staff in the grade.

    E=6000(4)=24000//

    (b) Find the number of staff in the grade when the, monthly expense is $54,000.

    E=54000

    6000n=54000

    n=9

    so , there are 9 staff

    2008-07-15 15:19:20 補充:

    2. The value of a car $C varies inversely as the number of years n for which it has been used. If the value of a car in the year 2004 after it has been used for 2 years is $25,000.

    (a) express C in terms of n.

    Ans:

    let C=k/n

    25000=k/2

    k=50000//

    so C=50000/2//

    2008-07-15 15:19:23 補充:

    (b) find the value of the car in the year 2007.

    Ans:years has been used = 2007-2004=3

    so C=50000/3=16666.7//

    2008-07-15 15:22:45 補充:

    3.Let C(average cost)=k1+k2/P(head)

    when P=144 , C=17

    17=k1+k2/144--(1)

    when P=168 , C=16

    16=k1+k2/168--(2)

    solve (1) ,(2), k1=10 ,k2=1008//

    So,C=10+1008/P

    2008-07-15 15:23:21 補充:

    (b.) How many students would be required to reduce the cost of lunch to $14?

    14=10+1008/P

    4=1008/P

    P=252//

    2008-07-15 15:24:54 補充:

    (c.) If 1000 students would take lunch, a rebate of $500 would be given to the school. Calculate the actual average cost per head.

    average cost without rebate=10+1008/1000=11.008

    total=1.1008*1000=1100.8

    after rebate=1100.8-500=600.8//

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