Question

A fraction, a/b, not necessarily in lowest terms is equivalent to 5/9. When 5 is added to the denominator of a/b, the value of the new fraction becomes equivalent to 1/2. What is the sum of a and b? A fraction, a/b, not necessarily in lowest terms is equivalent to 5/9. When 5 is added to the denominator of a/b, the value of the new fraction becomes equivalent to 1/2. What is the sum of a and b? @Mathematics

Answer 1

a/b = 5/9
a/(b+5) = 1/2

a = (5b)/9
\[\frac{5b}{9}\div (b+5)\]

Answer 2

a/(b+5) = 1/2 and a/b = 5/9
2a=b+5 9a=5b b = 9a/5 Substitute in 2a = b+5 and get 2a=9a/5 +5
1/5 a = 5, and a = 25 b = 9(25)/5 = 45. so a + b = 25 + 45 = 70