ok i kept playing with it and figured out one value for b could be 180 and one value for a could be 140, the sum would be less then 400 and the ratio satisfies the 7/9 proportion. but it took a while to come to that solution.....

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- December 11th 2011, 09:57 AM #1

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## what is one possible value for a+b

if a is divisible by 2, b is divisible by 5 and a/b=7/9, where a and b are positive numbers, and a+b<400, what is one possible value of a + b?

ok im not sure how to set this up...i would try to do this one by plug and chug.

i would try to find a number that was even and one that was odd whose sum would be less then 400.

so i dunno, one number has to be divisible by 5? let that number be 60 and the other number has to be divisible by 2 so it would be 330?

ok but a/b has to be 7/9 so whatever value i selected for a or b i would substitute and then solve.

so i would keep playing with the number until i got something that worked. my problem is time, i dont have time to plug and chug. so is there a faster way i can do this problem

- December 11th 2011, 10:01 AM #2

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## Re: what is one possible value for a+b

ok i kept playing with it and figured out one value for b could be 180 and one value for a could be 140, the sum would be less then 400 and the ratio satisfies the 7/9 proportion. but it took a while to come to that solution.....

- December 11th 2011, 10:03 AM #3
## Re: what is one possible value for a+b

a/b = 7/9 means that 9a = 7b

Now, a is even, so 9a = 7b can be rewritten as 18k = 7b for some k.

That b is divisible by 5 means that we can rewrite as 18k = 35j for some j.

k = 35 and j = 18 gives us

a = 70 and b = 90.