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
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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) (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
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