# algebra!!

posted by .

How many ordered pairs of integers (a,b) are there such that 1/a+1/b=1/200?

• algebra!! -

multiply both sides by 200ab
200b+200a = ab
200b - ab = -200a
b(200-a) = -200a
b = -200a/(200-a) = 200a/(a-200)
or
a = 200b/(b-200)

let a = 201, then b = 40200
let a = 199 , then b = -39800
let a = 202 , then b = 20200
let a = 198 , then b = -19800
let a = 203 , then b = not an integer !
let a = 197 , then b = not an integer!
let a = 204 , then b = 10200
let a = 205 , then b = 8200
let a = 206 , then b = not an integer, ahhh!
...
let a = 240, then b = 1200
let a = 600 , then b = 240000
let a = 10200 , then b = 204

we have to have (a-200) be divisible into 200a
obviously we cannot use a = 200, but we can go up or down from 200 leaving divisors of ±1 , ±2, ±4, ±5, ±8, ±10, .. as long as that divisor divides evenly into 200a
that is, 200 = 2x2x2x5x5

Wolfram says that there are 69 of these

http://www.wolframalpha.com/input/?i=%28x%2By%29%2F%28xy%29+%3D+1%2F200

• algebra!! -

This problem has been posted on Brilliant as a current problem in this weeks' Geometry problem set.

I am unable to post an image or internet link to it.

I ask that moderators take this posting down.

- Calvin Lin
Brilliant Challenge Master

## Similar Questions

1. ### Algebra

3x - 2y = 6 , 2x + 3= 6 are perpendicular lines but i need 3 ordered pairs for each. I used the m= y2-y1/x2-x1 method to establish that the slopes = -1. Any suggestions for ordered pairs for each line is much appreciated.
2. ### algebra

Provide an example of at least five ordered pairs that do not model a function. The domain will be any five integers between 0 and 20. The range will be any five integers between -10 and 10.
3. ### math

Find all the ordered pairs of integers such that x^2 - y^2 = 140 Any help or explanations would be wonderful!
4. ### Algebra

The ordered pairs represent values for x and y. (1,1) is x =1 and y=1. Substitute these ordered pairs in the equations and evaluate to see if are true. Then, graph the points and line to find another solution.
5. ### Math/ Algebra

Give an example of a function using a set of at least 4 ordered pairs. The domain will be any four integers between 0 and +10. The range will be any four integers between -12 and 5. Explain why your example models a function. Give …
6. ### math

How many ordered pairs of integers (x,y) are there such that 2x2−2xy+y2=225?
7. ### Math (Algebra)

How many ordered pairs of integers (x,y) are there that satisfy |x|+|y| ≤ 10?
8. ### number theory, math

How many ordered pairs of positive integers (a,b) are there such that (4a-1)/b and (4b-1)/a are both integers?
9. ### Number Theory.,Math

How many ordered pairs of positive integers (a,b) are there such that (4a-1)/b and (4b-1)/a are both integers?
10. ### College Algebra

give the domain and the range for the following set of ordered pairs and determine if the ordered pairs represent a function. A) (1,2)(3,4)(5,5)(4,4)(5,4) B) (4,1)(5,1)(6,1)(7,1)(8,1)

More Similar Questions