F.2 Maths 2 questions

1. let the son's age is x
5x-x=36
4x=36
x=9
so the son is 9 years old and father is 5x9=45years old

2.
let the tens digit be x and the unit digit be y
x+y=15...........(1)
(10y+x)-(10x+y)=27.............(2)
x+y=15
x=15-y.............(3)
put (3)into (2)
(10y+15-y)-[10(15-y)+y]=27
10y+15-y-150+10y+y=27
18y-135=27
18y=162
y=9
x+9=15
so x=6 y=9
test:96-69=27

3.
z+x=4............(1)
(100z+10y+x)-(100x+10y+z)=198.............(2)
x=4-z..............(3)
put (3)into(2)
100z+x-100x-z=198
100z+4-z-100(4-z)-z=198
198z-396=198
z=3
so x=1
the number is 1x3
after interchange is 3x1
x can be any number

4.x+4 2
------- = ---------
x+4+4 3

3x+12=2x+16
x=4

so it is 4/8

let x be the present age of Mr.lee , y be that of his son
[5y=x----------------(1)
[x-y=36--------------(2)

Sub. (1) into (2)
x-y=36
5y-y=36
4y=36
y=9

Sub. y=9 into (1)
5y=x
5(9)=x
x=45

.'.Mr. Lee is 45 years old and his son is 9 years old

2) let x be the ten digit and y be the unit digit
[x+y=15-----------------(1)
[(10y+x)-(10x+y)=27----------(2)
From (2), 9y-9x=27
y-x=3------------(3)

(1)+(3):2y=18
y=9

Sub. y=9 into (2)
(10y+x)-(10x+y)=27
9y-9x=27
9(9)-9x=27
9x=54
x=6
.'.the number is 69

3) let a be the hundreds digit , b be the ten digit and c be the unit digit
[(100c+10b+a)-(100a+10b+c)=198-----------------(1)
[a+c=4-----------------------------------------------------(2)

From (1), 99c-99a=198
c-a=2--------------------(3)
(2)+(3): 2c=6
c=3

Sub. c=3 into (2)
a+c=4
a+3=4
a=1

.'.the hundreds digit is 1 and the unit digit is 3


4) let x be the denominato and y be the numinator
[x-y=4--------------------------------------(1)
[(y+4) / (x+4)=2/3---------------(2)
from (2), 3y-2x=-4-------(3)
(1)x2: 2x-2y=8------(4)
(4)+(3): y=4
Sub. y=4 into (1)
x-y=4
x-4=4
x=8
.'. the fraction is 4/8........................????

1.
5x-x=36
x=9
therefore, the age of the son is 9, father is 45-year-old

2. let the 2-digit number is xy
x+y=15 ==>y=15-x
10y+x=10x+y+27
9y=9x+27
y=x+3
15-x=x+3
12=2x
x=6
therefore, x=6, y=9, the number is 69

3.let the 3-digit number is xyz
x+z=4 ==> z=4-x
100z+10y+x=100x+10y+z+198
99z=99x+198
z=x+2
4-x=x+2
2=2x
x=1
therefore, x=1, z=3

1 let the age of the son for Mr. Lee be Y

5Y-Y=36
4Y=36
Y=9

Therefore his son is 8 years old and Mr. Lee is 45 years old

2. The two Digits number is 6 and 9