Question

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

Answer 1

7/3

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 b

numerator: b(a/b + 1)

denominator: b(a/b - 1)

Put them together

The 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) = 7/2

Denominator: 5/2 - 2/2 = 3/2

numerator over denominator = 7/2 // 3/2 = 7/2 * 2/3 = 7/3

Answer: 7/3

Answer 2

7/3

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 b
• numerator: b(a/b + 1)
• denominator: b(a/b - 1)
• Put them together
• The 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) = 7/2
• Denominator: 5/2 - 2/2 = 3/2
• numerator over denominator = 7/2 // 3/2 = 7/2 * 2/3 = 7/3

Answer: 7/3

Nice problem: Thanks for posting.