幫我計2題代數既應用題.........

第1題:
Let the 2-digit no. be 10a + b
Given the no. is divisible by both 2 and 5,
Because 2 * 5 = 10, the no. is a multiple of 10
Therefore, b = 0
Given ½ (10a + b) = 6a - 4
½ (10a + b) x 2 = (6a - 4) x 2
10a + b = 12a - 8
8 = 2a
4 = a
a = 4
10 a + b = 10 * 4 + 0 = 40

Ans. The 2-digit number is 40.

第2題:
Let (a) be the no of chicken
Let (3b) be the no of rabbits

equation 1 : a + 3b = 35
equation 2 : 2a + 3b + 2b x 4 = 90 ( where 3b means 1/3 of the rabbits with 3 legs;
2b means 2/3 of the rabbits; 4 is 4 legs)

From equation 1
a + 3b = 35
a = 35 - 3b

From equation 2

2a + 3b + 2b x 4 = 90
2(35 - 3b) + 3b + 8b = 90
70 - 6b + 11b = 90
70 - 6b + 11b + 70 = 90 + 70
5b = 20
5 = 4


(b) The nunmber of rabbits with 4 legs is 8

(a) Since a = 35 - 3b
Therefore a = 35 - 3(4)
a = 35 - 12
a = 23

The number of chicken is 23.

第1題:
A 2-digit number is divisible by both 2 and 5. Half this number is less than 6 times the then digit of the number by 4. Find this 2-digit number.

Let the 2-digit no. be 10a + b
Given the no. is divisible by both 2 and 5,
Because 2 * 5 = 10, the no. is a multiple of 10
Therefore, b = 0
Given ½ (10a + b) = 6a - 4
10a + b = 12a - 4
4 = 2a
2 = a
a = 2
10 a + b = 10 * 2 + 0 = 20

Ans. The 2-digit number is 20.

第2題:
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 number of legs is 90, find the number of.....
(a) chickens,
(b) rabbits with 4 legs

Let the no. of chickens be a
Let the no. of rabbits be b
Thus, the no. of 3-leg rabbits = 1/3b
Thus, the no. of 4-leg rabbits = 2/3b
Given a + b = 35
That is a = 35 - a
Given 2a + 3(1/3 b) + 4(2/3 b) = 90 ……(i)
Put a = 35 - b into (i), we get
2(35 - b) + 3(1/3 b) + 4(2/3 b) = 90
24(35 - b) + 12b + 32b = 90 * 12
840 - 24b + 12b + 32b = 1080
20b = 240
b = 12
2/3 b = 2/3 * 12 = 8
a = 35 - a = 35 - 12 = 23

Ans. The no. of chickens is 12 and the no. of 4-leg rabbits is 8.

2006-11-06 13:58:08 補充：
Assume your (then digit) is (tenth digit).