f.3 數學 Linear inequalities in one unknown

Perrie

2008-04-14 4:48 am

1.The total cost of 3 watermelons and 6 apples is not greater than $120. If the cost of a watermelon is $30 and it is $x higher than that of an apple, find the least value of $x.
2. There are 2 consecutive positive odd numbers. the sum of the smaller number and one-third of the larger number is less than or equal to 10. find the possible values of the smaller number.
3. there are 600 rabbits and chickens in a farm. if the total number of their legs is not less than 1500, at least how many rabbits are there?

回答 (1)

用戶232127

2008-04-14 5:22 am

✔ 最佳答案

1.根據題意列式
3(30)+6(30-x)<=120
180-6x<=30
6x>=150(不等式兩邊乘以或除以負數要轉不等號,即>轉<,<轉>)
x>=25
i.e. least value of $x is $25

2.let the 2 numbers be x and x+2 respectively(連續奇數必然相差2,所以設較大那數為x+2)
x+(x+2)/3 <= 10
(4x+2)/3 <= 10
4x+2 <= 30
4x <= 28
x <= 7
i.e. x = 1or3or5or7(要為正,且為奇數,x取值只能是這4個)

3.note that rabbits and chickens have 4 legs and 2 legs respectively
let the number of rabbits be x and that of chickens be y
x+y = 600------------(1)
4x+2y >= 1500------(2)
(1):y=600-x---------(3)
sub(3)into(2):
4x+2(600-x) >= 1500
1200+2x>=1500
2x>=300
x>=150
i.e. least possible number of rabbits is 150

2008-04-13 21:23:54 補充：
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2008-04-13 21:24:27 補充：
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