F.5 Variation

2012-10-10 7:43 am

1.The total expenses($E) of running a birthday party is partly constant and partly varies directly as the number of guests(N) in the party.When N=30,E=1500;when N=40,E=1850.
a)express E in terms of N
b)if 50 guests come to the party,what is the average expense per guest?
c)if the average expense per guest is $40,how many guest come to the party?

2.if (2a-b):(a+b) =2:3,then find a : b

3.let x : y =2 : 1 and y : z=3 : 2,find the value of (x-z)/(2z-y)

回答 (1)

用戶2053

2012-10-10 10:47 am

✔ 最佳答案

1a)Let E = C + kN , (where C and k are constants)By given ,1500 = C + 30k ... (1)
{
1850 = C + 40k ... (2)(2) - (1) :
1850 - 1500 = 40k - 30k
k = 35Substitute into (1) :
1500 = C + 30*35
C = 450∴ E = 450 + 35N
b)Total expenses($E)
= 450 + 35(50)
= $2200The average expense per guest
= 2200 / 50
= $44
c)(450 + 35N) / N = 40
450 + 35N = 40N
5N = 450
N = 90There are 90 guest come to the party if the average expense per guest is $40.
2) (2a - b) : (a + b) = 2 : 3
3(2a - b) = 2(a + b)
6a - 3b = 2a + 2b
4a = 5b
a : b = 5 : 4
3)x : y = 2 : 1 = 6 : 3
and y : z = 3 : 2∴ x : y : z = 6 : 3 : 2 Let x = 6k , y = 3k , z = 2k , (were k is non zero constant)(x - z) / (2z - y)
= (6k - 2k) / (2*2k - 3k)
= 4k / k
= 4

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