Question

for certain positive integers a and b, 2/A+1/B=13/15. What is A+B

Answer 1

Answer:  8

=====================================================

Explanation:

Simplify the left hand side to get

$\frac{2}{A}+\frac{1}{B} = \frac{13}{15}\\\\\frac{2B}{AB}+\frac{A}{AB} = \frac{13}{15}\\\\\frac{2B+A}{AB} = \frac{13}{15}$

Compare the denominators AB and 15.

If AB = 15, then we could have,

• A = 1, B = 15
• A = 3, B = 5
• A = 5, B = 3
• A = 15, B = 1

Through trial and error, the only solution is A = 3 and B = 5 because 2B+A = 2*5+3 = 10+3 = 13 to match the numerator on the right hand side.

Therefore, A+B = 3+5 = 8