Question

The ratio of the sum of two positive integers to their difference is 7:5. If the the sum of the two numbers is at most 25, find all possible values for the pair of numbers.

Answer 1

ok got it

Answer 2

write it out first as such: \[\huge \frac{m+n}{m-n}=\frac{7}{5}\]

Answer 3

Then include this: \[\huge 0<m+n \le25\]

Answer 4

Simplifying the first equation gives \[\huge m=6n\]

Answer 5

find all possible values of that in the interval now

Answer 6

I believe there are 3 sets (a, b)

Answer 7

We know that \(n\leq m\), because the ratio is positive.

Answer 8

i believe it should be \[\huge n<m\]

Answer 9

but same idea

Answer 10

Hint: try \[\huge n=1, 2, 3....\]

Answer 11

Thanks @Rizags

Answer 12

np