SOLUTION: In a certain positive fraction a/b, the numerator is 2 less than the denominator. If the numerator and denominator are interchanged, the fraction is increased by 1 1/15. Fin

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Question 772707: In a certain positive fraction a/b, the numerator is 2 less than the denominator. If the numerator and denominator are interchanged, the fraction is increased by 1 1/15. Find a+b.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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In a certain positive fraction a/b, the numerator is 2 less than the denominator.
a = b - 2
:
If the numerator and denominator are interchanged, the fraction is increased by
1 1/15. Find a+b.
a%2Fb + 16%2F15 = b%2Fa
:
multiply by 15ab, resulting in
15a^2 + 16ab = 15b^2
:
replace a with (b-2)
15(b-2)^2 + 16b(b-2) = 15b^2
15(b^2 - 4b + 4) + 16b^2 - 32b = 15b^2
15b^2 - 60b + 60 + 16b^2 - 32b = 15b^2
;
combine like terms on the left
15b^2 - 15b^2 + 16b^2 - 60b - 32b + 60 = 0
16b^2 - 92b + 60 = 0
;
simplify, divide by 4
4b^2 - 23b + 15 = 0
:
Factors to
(4b-3)(b-5) = 0
:
two solutions
b = 5 is the only integer solution
then
a = 5 - 2
a = 3
therefore
a + b = 8