F.2 simultaneous equation

1） x/2+y/3=13 (1)
x/3-y/4=3(2)

from (1)
3x/6 + 2y/6 = 13
3x + 2y = 78
9x + 6y = 234(3)

from (2)
4x/12 + 3y/12 = 3
4x + 3y = 36
8x + 6y = 72(4)

(3) - (4)
==> x = 162
sub into 3x + 2y = 78
(3)(162) + 2y = 78
==> y = -204

2） x and y are two numbers in the ratio of 5:1 and x is also 9 more than twice y. Find the values of x and y.

x/y = 5/1
x = 5y(1)
x - 2y = 9(2)

from (2) x = 9+2y
sub into (1)
9 + 2y = 5y
9 = 3y
y = 3
x = 9 + 2y
x = 9 + (2)(3)
x = 15

3) Alan is 30 years younger than his father.4 years ago,his age was 1/16 his
father's.Find their present age.

Let Alan is x years old at present.
His father is x+30 at present

4 years ago. Alan was x-4 years old
His father was x+30-4 = x+26

(x-4)/(x+26) = 1/16
(16)(x-4) = (x+26)
16x - 64 = x + 26
15x = 90
x = 6

Alan is 6 years old
His father is 36

4 years ago
Alan was 2 years old
His father was 32
2/32 = 1/16


4) A man rows a boat 30 km downstream in 30 minutes. The return trip takes 1 hours.
a） At what speed(in km/h) does the man row in still water?

Let the man can row with speed x
stream speed be y

speed X time = distance

(x+y)(0.5) = 30
(x+y) = 60(1)
(x-y)(1) = 30(2)

(1) - (2)

2y = 30
y = 15
x = 45

The man can row 45 km/h in still water
b） What is the speed(in km/h) of the stream?

speed of the stream = 15 km/h

5)Peter and James have x marble altogether.When Peter gives 4 marbles to James,then they have the same number of marbles.Find the value of x.

6) Johnny was born in 1x8y. Find the year that Johnny was born according to the following information.
1) In the year 2004,Johnny's age will be the sum of the four digits of the year that he was born.
2) In the year 2022,Johnny's age would be 4x+y.

from 1) 2004 - (1000+100x+80+y) = 1+x+8+y
2004 - 1000 - 100x - 80 - y = 9 + x + y
924 - 100x - y = 9 + x + y
915 = 101x + 2y

from 2)
2022 - (1000+100x+80+y) = 4x + y

OK ! That is all
Do something yourself.