Problem: If ba=2\dfrac{b}{a}=2ab=2 and cb=3\dfrac{c}{b}=3bc=3, what is the ratio of a+ba+ba+b to b+c?b+c?b+c?
Answer Choices:
A. 13\dfrac{1}{3}31
B. 38\dfrac{3}{8}83
C. 35\dfrac{3}{5}53
D. 23\dfrac{2}{3}32
E. 34\dfrac{3}{4}43
Solution:
c=3b=3(2a)=6ac=3 b=3(2 a)=6 ac=3b=3(2a)=6a, so
a+bb+c=a+2a2a+6a=38\dfrac{a+b}{b+c}=\dfrac{a+2 a}{2 a+6 a}=\dfrac{3}{8} b+ca+b=2a+6aa+2a=83