If the ratio of two numbers is 5: 2, what is the ratio of their sum to their difference?

7/3

Step-by-step explanation:

Let the two numbers be x and y which are relatively prime to each other.

a/b = 5/2

So you want the ratio of

(a + b) / (a - b)

Take out a common factor of bnumerator:  b(a/b + 1)denominator: b(a/b - 1)Put them togetherThe b's cancel out (a/b + 1) / (a/b - 1)but a/b = 5/2(5/2 + 1) / (5/2 - 1)Numerator:  (5/2 + 2/2) = 7/2Denominator: 5/2 - 2/2 = 3/2numerator over denominator = 7/2 // 3/2 = 7/2 * 2/3 = 7/3

7/3

Nice problem: Thanks for posting.