Maths Problem!

63 can be written as
10*6 + 3

And 36 can be written as
10*3 + 6,

So, how can we write XY and YX in this form?

When u have done this, you will have an equation to solve. I expect that you will need to read this, to help u solve the equation.

Reply 2

OP

10x+y
10y+x

Reply 3

kamsingh

10x+y
10y+x

Right, so now u can form an equation
Tomorrow its his birthday, so he will be one year older, and then he will be half the age of his dad.

Reply 4

OP

10x+y= 2(10y+x+1)
10x+y= 20y+2x+2
8x-19y=2

Reply 5

kamsingh

10x+y= 2(10y+x+1)
10x+y= 20y+2x+2
8x-19y=2

Not quite, you have mixed up the father and sons ages.

The equation should be
10y + x = 2(10x+y+1)
19x - 8y = -2

Reply 6

OP

oh yeah sorry, now whats next?

Reply 7

kamsingh

oh yeah sorry, now whats next?

Now, to solve this, you need to read this.

Meepmeep, how did you get simultaneous equations?

Reply 8

OP

thats what i wanna know how did he get them simultaneous, and that site looks like a bunch of jibberish to me!

Reply 9

meepmeep

JamesF

Now, to solve this, you need to read this.

Meepmeep, how did you get simultaneous equations?

Sorry, read it wrong. Didn't look properly and thought they were two independant equations.

Reply 10

kamsingh

thats what i wanna know how did he get them simultaneous, and that site looks like a bunch of jibberish to me!

Lol, ok, well, that would be how u solve it.
This site can save u the fuss of doing it urself.

Plug in the numbers and you get
x = 2 + 8t
y = 5 + 19t

For all integers t.
Remember that x and y must be less than 10, so the only solution is therefore when t = 0, so
x = 2, y = 5.

Reply 11

meepmeep

kamsingh

if my age is XY, and my fathers YX, (the digits are reversed eg 36, and 63 etcc) and tommorow its my birthday,and my father says hey your age is half of my age, how would u figure this out alegbraically, and not through trial and error?

2(10x + y + 1)=10y + x
20x + 2y + 2 = 10y + x
19x - 8y = -2
Thus - 8y = -2 - 19x
So y = (2+19x)/8

Try values of x from 1 to 9 (as y has to be a whole number):

When x=1, y=21/8
When x=2, y=5
When x=3, y=59/8
When x=4, y=78/8
When x=5, y=97/8
When x=6, y>10 and as y is just a digit, no value of x bigger than 5 can give a solution, so the only solution is x=2, y=5. In other words, you are 25 and your father is 52.

Reply 12

OP

meep meep, trial and error is always the weak way out, i knew u could do it via trial and error, but james method is much more stronger.

Reply 13

meepmeep

kamsingh

meep meep, trial and error is always the weak way out, i knew u could do it via trial and error, but james method is much more stronger.

Yep, agreed. However, for this problem, it is perfectly adequate to take a trial and error approach as you only have a very small number of possibilities (as you are restricted to single digit integer solutions), although if you had a wider problem, of course an algebraic solution would be prefered (and is more elegant).

Reply 14