Chaib Ratios

Suppose quantities ratios  
\[A\]
  and  
\[B\]
  are in the ratio  
\[3:5\]
. Ratios  
\[B\]
  and  
\[C\]
  are in the ratio  
\[2:7\]
.
What is the ratio  
\[A:B:C\]
?
Multiply the first ratio by 2 to get  
\[6:10\]
  and the second by 5 to get  
\[10:35\]
. The relative quantities for  
\[C\]
  are the same in both equations, so we can write the ratio  
\[A:B:C\]
  as  
\[6:10:35\]
.