# Homework Help: Problem about equation solving

1. Jul 25, 2017

### OcaliptusP

1. The problem statement, all variables and given/known data
What is x ?( Assuming x and y are positive)
2. Relevant equations
1000/x=3600 + (3600(y-x)+1000)/x+y

3. The attempt at a solution

Calculator gives it as x=5/36 but I cannot find a way to get that?

2. Jul 25, 2017

### Ray Vickson

Do you mean
$$(1): \; \;\; \frac{1000}{x} = 3600 + \frac{3600(y-x) +1000}{x} + y$$
or do you mean
$$(2): \; \;\; \frac{1000}{x} = 3600 + \frac{3600(y-x) +1000}{x+ y}$$
In either case you have only one equation in two unknowns $x$ and $y$, so there will generally be an infinite number of different solutions. For example, if you put $y=0$ you will get one solution $x$, if you put $y = 1000$ you will get a different solution $x$, and so forth. Are you sure you have not left out some important information?

3. Jul 25, 2017

### haruspex

In general, yes.
But here we are given x and y both positive. (1) has no solutions, but (2) has only the given solution for x (y being indeterminate).
Just multiply it out and simplify. Post your working as far as you get.

4. Jul 26, 2017

### OcaliptusP

It's the second one. I put it on the calculator and give the result as x=5/36?
I simplified until x/5=x/36y+ 1/36 but cannot get further

Last edited by a moderator: Jul 26, 2017
5. Jul 26, 2017

### haruspex

6. Jul 26, 2017

### cnh1995

There is no y in the final equation.
Post your working so we can see where you went wrong.

7. Jul 26, 2017

### OcaliptusP

Well starting equation was:
1000/x=3600+(3600(y-x)+1000)/(x+y)
Divide all 200
5/x=18+(18(y-x)+5)/(x+y)
Can be written as;
5/x=18+(18y-18x+5)/(x+y)
Multiply 18 with (x+y)/(x+y)
5/x=(18x+18y+18y-18x+5)/(x+y)
5/x=36y+5/(x+y)

8. Jul 26, 2017

### OcaliptusP

Yes it was wrong as I noticed, I've sent my final work

9. Jul 26, 2017

### haruspex

Continue to simplify. Multiply out.

10. Jul 26, 2017

### OcaliptusP

Okay I've missed the detail. Thanks for all your help

11. Jul 26, 2017

### OcaliptusP

If we continue
5x+5y= 36xy + 5x
Then x=5/36

12. Jul 26, 2017

### OcaliptusP

Can you explain why do we need information of x and y is positive to derivate that?

13. Jul 26, 2017

### haruspex

No, my post#3 was a bit misleading there. That comment only appiled to the other interpretation of the equation given, i.e. (1) in Ray's post.

14. Jul 26, 2017

### OcaliptusP

Okay. Thanks to everyone who helped.