代數題(20分)(長答的)

1)
Assume that the 2-digit number is AB
Since it is divisible by both 2 and 5, the value of B must be 0
(You know that B is either 5 or 0, but B must be even number because AB is divisible by 2)
Therefore we can rewrite it as A0.
==> The true value of A0 is 10A + 0 = 10A

According to the question,
10A / 2 = 6A - 4
5A = 6A - 4
4 = A

Thus, the 2-digit number is 40

2a)
Let x be the number of chicken while y be the number of rabbits
Total number of heads = 35
Thus,
x + y = 35 -- (1)
Total number of legs is 90
Thus,
2x + 2/3y(4) + 1/3y(3) = 90
2x + 8y/3 + y = 90
6x + 8y + 3y = 270
6x + 11y = 270 -- (2)

From (1)
x = 35 - y -- (3)
Put (3) into (2)
6(35-y) + 11y = 270
210 - 6y + 11y = 270
5y = 60
y = 12
Put y=12 into (3)
x = 35-12
x = 23

Thus, the number of chickens is 23

2b)
From 2a) y = 12
There are 12 rabbits in total
SInce 1/3 have 3 legs, it means 2/3 of rabbits have 4 legs
Therefore,
12 * 2/3
= 8
There are 8 rabbits with 4 legs

1.
Let the tenth digit be X and the unit digit be Y

Since the number is divisible by 5 ====> Y = 5 or 0
Since the number is divisible by 2 ====> Y = 0

(10X + Y)/2 = 6X - 4 ============> X = 4
Therefore the 2-digit number is 40

2.
Let the number of rabbits be X and the number of chickens be Y
Then
X + Y = 35 ................................... (1)
and
3X/3 + 4X(1 - 1/3) + 2Y = 90 ===> 11X/3 + 2Y = 90 ====> 11X + 6Y = 270 .........(2)

(2) - (1) x 6 gives 5X = 60 ========> X = 12
rabbit with 4 legs = 2X/3 = 8
Sub X in (1) gives Y = 23

Therefore there are 23 chickens and 8 rabbits with 4 legs