急急急!!!!!!!!!!!!!!!!!數學題math~~~~30點~~~

>>>1)A 2-dight number is divisble by both 2 and 5.Half this number is less than 6 times the tens dight of the number by 4.Find this 2-dight number.(use equation)


果個係digit, 係咪?

(1)首先假設左未知數先,
設 x 為這個數值的個位, y 為這個數值的十位
Let x be the lower digit and y be the tens digit.

換句話講, 呢個數既值就係 10x+y



(2)然後以x, y 表示題目的意思
"A 2-dight number is divisble by both 2 and 5."
有個兩位數, 可以被2同5除盡.

10x + y = 2 * 5K = 10K where K is a constant.
Therefore, y=0


"Half this number is less than 6 times the tens dight of the number by 4."
這個數值的一半比它的十位數值的6陪小於4.
10x / 2 = 6x + 4
5x = 6x + 4
x = 4

(3)"Find this 2-dight number"
Therefore, the 2-digit number is 40.




>>2)There are some chickens and rabbits in a cage.1/3 of the rabbits were born to have 3 legs.If the total number of heads is 35 and the total of legs is 90,find the number of
a.chickens(use equation)
b.rabbit with 4 legs

Let a be the number of the chickens and
b be the number of rabbits

total number of rabbit legs = b/3 * 3 + 2b/3 * 4 = 11b/3
total number of chicken legs = 2a
Therefore, 2a + 11b/3 = 90 -----------[1]

total number of heads = a + b = 35
so, a = 35 - b -------------------------[2]

Put [2] into [1],
2(35-b) + 11b/3 = 90
70 + 5b/3 = 90
5b/3 = 20
b = 12 ----------[3]
Put [3] into [2], a = 35 - 12 = 23

(a)There are 23 chickens.

(b)2(12)/3 = 8
There are 8 rabbits with 4 legs.

Since the number is divisible by both2 and 5, the unit digit must be 0, so let the number be x0.
Half of this number is 10x/2 = 5x.
6 times the tens digit = 6x.Therefore,
5x + 4 = 6x
x = 4. the number is 40.
2) Let number of chicken = x
number of rabbits = (35 -x) because there are 35 heads.
Number of chicken legs = 2x.
Number of rabbit with 4 legs = 4[2(35-x)/3] = 8(35-x)/3.
Number of rabbits with 3 legs = 3[(35-x)/3] = (35-x).
Total number of legs = 90, therefore,
2x + 8(35-x)/3 + (35-x) = 90
6x + 280 - 8x + 105 - 3x = 270
-5x + 385 = 270
5x = 115
x = 23 = number of chicken. Number of rabbits = 35- 23 = 12.

2008-10-21 17:19:34 補充：
Number of rabbits with 4 legs = (2/3)(12) = 8.