SOLUTION: a/b is a fraction. If 2 is added to the numerator, the value of the fraction is 1/2. I f 3 is added to the denominator, the fraction has a value of 1/3. What is the value of the su

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: a/b is a fraction. If 2 is added to the numerator, the value of the fraction is 1/2. I f 3 is added to the denominator, the fraction has a value of 1/3. What is the value of the su      Log On


   

Question 37162: a/b is a fraction. If 2 is added to the numerator, the value of the fraction is 1/2. I f 3 is added to the denominator, the fraction has a value of 1/3. What is the value of the sum a+b?
Answer by wuwei96815(245) About Me  (Show Source):
You can put this solution on YOUR website!
This problem can be solved by substitution because you have two unknowns and two equations.

Solve the first equation for b:
a+2/b = 1/2
2a+4 = b

Substitute the found value for b into the second equation:
a/b+3 = 1/3
a/2a+4+3 = 1/3
3a = 2a + 7
a = 7

Now substitute the found value for a into the first equation:
2a+4 = b
2(7)+4 = b
18 = b

a+b = 7+18 = 25