一堆代數題(20分)(急!!!!!!!!!!!!)

1. A
1/3(4t + 3) = 1/2(3t - 1)
1/3(4t + 3) * 6 = 1/2(3t - 1) * 6
2(4t + 3) = 3(3t - 1)
8t + 6 = 9t - 3
6+3=t
t=9

2. B
1 - x/2 - x/4 - x/8 = x - 1
(1 - x/2 - x/4 - x/8)*8= (x - 1)*8
8 - 4x - 2x - x = 8x -8
16 = 15x
x=16/15

3.Thomas is 15 years older than his sister. Five years later, he will be twice as old as his sister. Find their present ages.
Let x be the predsent age of Thomas.
Then the predsent age of Thomas' sister = (x-15)
x+5=2*{(x-15)+5}
x+5=2*(x-10)
x+5=2x-20
x=25
The predsent age of Thomas is 25.
The predsent age of Thomas' sister is 10.

1. It is ture that 1/3(4t + 3) = 1/2(3t - 1) when t = A
A. 9
B. 8
C. 6
D. -6

2. if 1 - x/2 - x/4 - x/8 = x - 1 , then x = B
A. 8
B. 16/15
C. 8/9
D.1/7


1. Thomas is older than his sister. Five years later, he will be twice as old as his sister. Find their present ages.

Sol: Let x be the age of Thomas , then ( x - 15 ) be the age of his sister.

2(x -15 ) = 15+5
2x - 30 = 20
2x = 20+30
2x = 50
x = 50/2 ←-------------------------- ( 50/2 = 50除 2 )
x = 25//
and 25 - 15 = 10//
.
. . The age of Thomas is 25 years old and the age of his sister is 10 years old .

P.S 因為哥哥的歲數再過5年就是妹妹的2陪﹐所以 2 ( x - 15 ) 。而後面則說明哥哥過5年的歲數﹐所以 =15+5 。

1. It is ture that 1/3(4t + 3) = 1/2(3t - 1) when t = ?

Ans:
1/3(4t + 3) = 1/2(3t - 1)
4t/3 + 1 = 3t/2 - 1/2
1 + 1/2 = 3t/2 - 4t/3
3/2 = (9t-8t) / 6
t = 9, i.e. A


2. if 1 - x/2 - x/4 - x/8 = x - 1 , then x = ?

Ans:
1 - x/2 - x/4 - x/8 = x - 1
1 - (4x + 2x + x)/8 = x - 1
1 - 7x/8 = x - 1
2 = x + 7x/8
2 = (8x + 7x)/8
16 = 15x
x = 16/15, i.e. B


Thomas is 15 years older than his sister. Five years later, he will be twice as old as his sister. Find their present ages.

Let Thomas be x years old and his sister be (x-15) years old
Five years later, Thomas be (x+5) years old, and his sister be (x-10) years old

(x+5) = 2 (x-10)
x+5 = 2x-20
x = 25

Therefore, Thomas is 25 years old and his sister is 10 years old