Discussion
If a, b, c are three numbers such that a:b = 5:9 and b:c = 27:35, find a:c.
Answer: A
The ratio a:c is 3:7.
Make the b terms equal. In the first ratio b is 9 and in the second 27, so multiply the first ratio by 3:
\[ \begin{aligned} a : b &= 5 : 9 = 15 : 27 \\ b : c &= 27 : 35 \\ a : c &= 15 : 35 = 3 : 7 \end{aligned} \]
7:3 inverts the ratio, and 4:7 and 7:4 do not follow from the given ratios.
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