Two numbers, a and b, have a ratio of 3 to 5. When 2 is added to each number, their ratio changes to 2 to 3. What is the value of b?

Explanation

Given the ratio a:b = 3:5, we can express a as (3/5)b. After adding 2 to both numbers, the ratio becomes (a+2):(b+2) = 2:3. Setting up the equation: 3(a + 2) = 2(b + 2). Substituting a = (3/5)b gives 3((3/5)b + 2) = 2(b + 2). Simplifying leads to 9b/5 + 6 = 2b + 4, which further reduces to 9b + 30 = 10b + 20. Solving for b results in b = 10.