SOLUTION: Correct Question :" Let a and b be distict real numbers for which a/b + (a+10b) / (b+10a) = 2 The value of a/b is a) .5 b) .6 c) .8 d) 1 or .8

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Correct Question :" Let a and b be distict real numbers for which a/b + (a+10b) / (b+10a) = 2 The value of a/b is a) .5 b) .6 c) .8 d) 1 or .8       Log On


   



Question 77271: Correct Question :"
Let a and b be distict real numbers for which
a/b + (a+10b) / (b+10a) = 2
The value of a/b is
a) .5 b) .6 c) .8 d) 1 or .8

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
a%2Fb+%2B+%28a+%2B+10b%29%2F%28b+%2B+10a%29+=+2
ab%2Fb+%2B+%28a+%2B+10b%29b%2F%28b+%2B+10a%29+=+2b
a+%2B+%28a+%2B+10b%29b%2F%28b+%2B+10a%29+=+2b
a%28b+%2B+10a%29+%2B+%28a+%2B+10b%29b%28b+%2B+10a%29%2F%28b+%2B+10a%29+=+2b%28b+%2B+10a%29
a%28b+%2B+10a%29+%2B+%28a+%2B+10b%29b+=+2b%28b+%2B+10a%29
ab+%2B+10a%5E2+%2B+ab+%2B+10b%5E2+=+2b%5E2+%2B+20ab
10a%5E2+-+18ab+%2B+8b%5E2+=+0
10a%5E2+-+10ab+-+8ab+%2B+8b%5E2+=+0
%2810a%5E2+-+10ab%29+%2B+%28-8ab+%2B+8b%5E2%29+=+0
10a%28a+-+b%29+-+8b%28a+-+b%29+=+0
%2810a+-+8b%29%28a+-+b%29+=+0
we get: 10a - 8b = 0
10a = 8b
a = .8b and b = 1.25a
a / b or .8b / 1.25a or .8(1.25a) / 1.25a = 0.8
we get: a - b = 0
a = b
a / b = b / b = 1
(d)