What is the simplified numerical value of (a + 11b)/(a - b) if (4a + b)/(a - 2b) = 5?
Well, I thought about it, couldn't figure it out, but here's a method you can use if you don't know how to do it.
Let's say a = 1,
(4 + b)/(1 - 2b) = 5
20 + 5b = 1 - 2b
7b = -19
b = -19/7
So we have a = 1, b = -19/7, plug that into this equation. :))
(a + 11b)/(a - b)
=^._.^=
(4a + b) / (a - 2b) = 5 cross-multiply
4a + b = 5 (a - 2b)
4a + b = 5a -10b
b + 10b = 5a - 4a
11b = a and a/b = 11 ⇒ b/a = 1/11
So
(a + 11b) / (a - b) =
1 1 1 2 2
________ = ______ = _______ = ______ = __________ =
( a - b) ( a - b) (a - b) (a - b) 1 - (b/a)
__________ ________ ______ ______
( a + 11b) (a + a) 2a a
2 2 2*11 22
_________ = _________ = ____ = ___ = 2.2
1 - 1/11 10 /11 10 10