Posted by **David** on Monday, August 4, 2014 at 10:00pm.

1. If b is a positive integer than 200, then how many integer pairs (a,b) satisfy the equation a/b= 2/9

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**Reiny**, Monday, August 4, 2014 at 10:35pm
I assume you meant:

If b is a positive integer < 200

a/b = 2/9

9a = 2b

a = 2b/9

So b must be a multiple of 9 to have a as an integer

the smallest value of b is 9

and the largest value of b is 198

so we have:

9 18 27 .... 180 189 198

to find out how many terms are in this arithmetic sequence ...

term(n) = a + (n-1)d

198 = 9 + (n-1)(9)

189 = 9n - 9

198 = 9n

n = 22

there are 22 such ordered pairs

check:

the pairs are (2,9) , (4,18) , (6,27) , ... (42, 189) , (44, 198)

in each case a/b = 2/9

e.g.1 :

27/6 = 2/9

189/42 = 2/9

....

etc

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