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​