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

1. ## 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

2. ## 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.....

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.