Question

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

Answer 1

Answer: 8

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Step-by-step explanation:

Simplify the left hand side to get

`(2)/(A)+(1)/(B) = (13)/(15)\\\\(2B)/(AB)+(A)/(AB) = (13)/(15)\\\\(2B+A)/(AB) = (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